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A PRACTICAL TREATISE 



OM 



LOCOMOTIVE ENGINES. 



PRACTICAL TREATISE 



ON 




LOCOMOTIVE ENGINES; 



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DUBINO A BE8IDENCB IN ENGLAND FOB SCIENTIFIC PUBP08ES. 
INCSBA8E0 BT A GBBAT MANY NEW BZPEBIMBNTS AND BB8EABCHE8. 



LONDON; JOHN WEALE. 
1840. 



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LONDON: 
W. HU0HB8, kino's HKAD COURTt OOUGH SQUARE. 



INTRODUCTION 

TO THE FIRST EDITION. 



Thebe exists no special work on locomotive engines. 
Two writers^ Wood and Tredgold,* have indeed, in Eng- 
land, slightly touched upon that matter, but only in a 
subordinate manner, in treatises on railways; and, be- 
sides, they both wrote at a time when the art was scarcely 
beyond its birth. Consequently their ideas, their cal- 
culations, and even the experiments they describe, have 
hardly any relation to the facts which actually pass before 
our eyes, and can be of no use to such as wish to acquire 
a knowledge of these engines and their employ on rail- 
ways. 

Many questions had not even been entered into, others 
had been solved in a faulty manner. New researches on 
the subject became therefore indispensable. This work 
will, in consequence, be found completely different from 

^ ' A Practical Treatise on Railroads, and Interior Commimi- 
cation in general, by Nicholas Wood.' 1st edition, London, 
1825; 2d edition, London, 1832. 

' A Practical Treatise on Railroads and Carriages, by Thomas 
Tredgold.' London, 1825. 



VI INTRODUCTION 

any thing that has been published hitherto. No facts will 
be quoted, but such as result from actual observation ; no 
experiments related, but those made by the author hunself, 
on a new plan, and with new aims; finally, no theory 
exposed, but such as is derived from those experiments. 

If at first sight it appear astonishing that no theory 
of locomotive engines should exist, the surprise ceases 
on considering that the theory of the steam engine 
itself, taken in general, has not yet been explained. It 
was natural to suppose, that, respecting a machine at 
present in such universal use, and on a subject of such 
importance, every thing had been said, and every expla- 
nation given long ago. Far from this being the case, 
however, not even the mode of action of the steam in 
these engines has been elucidated. In the absence of such 
indispensable knowledge, all theoretical calculations were 
impossible. Suppositions were put in the place of facts. 
In consequence, we have seen very able mathematicians 
propose, on the motion of the piston in steam engines, 
analytical formulee, which would certidnly be exact, if all 
things went on in the engine as they suppose ; but which 
not being founded on a true basis, fall naturally to the 
ground, in presence of facts. From this also results that, 
in practice, the proportions of the engines have only been 
determined by repeated trials, and that the art of con- 
structing them has proceeded hitherto in the dark, and by 
imitation. 

Locomotive engines being first of all steam engines, we 
cannot advance in the researches we undertake, without 
solving at the same time the question relating to steam 
engines in general. There is even a remarkable point to 



1 



} 



TO THE FIRST EDITION. VU 

be observed^ which is, that of all sorts of steam engines, 
locomotive ones are those which, in their application, have 
to overcome the least complicated resistance, and the most 
susceptible of a rigorous appreciation. This circumstance 
renders them therefore more proper than any others, for 
furnishing an explanation of general fetcts common to all 
those machines. The theory once satisfactorily established 
in regard to locomotive engines, wiU, of course, apply 
equally to all sorts of steam engines, and more especially 
to those which, like locomotive ones, work at a high 
pressure. 

We flatter ourselves, therefore, that our researches, A 

although apparently confined to locomotive engines, may 
at the same time illustrate the principal points of the 
theory of steam engines in general. 

However, in order to indicate clearly the design of this 
work, and to show in what it differs from those that have 
preceded it, we think proper to enter here into some 
particulars as to the points on which we have new re- 
searches to offer, either theoretical or experimental. It 
will be seen that those points embrace nearly the whole 
subject. 

The pressure of the steam in the boiler had been, till 
now, considered as invariable in every engine. It was 
calculated once for all, and by approximation, according 
to the weight on the valve. A great number of obser- 
vations will show, however, how much it varies during the 
motion of the engine, and how necessary it is to take that 
circumstance into consideration, and to make use of a 
more exact mode of determination, lest the calculation 
should be entirely founded on an erroneous basis. 



i 



i 



VIU INTRODUCTION 

The friction of the waggons was^ until now, valued much 
too high. This error naturally rendered every calculation 
false, by misleading with regard to the true resistance 
overcome by the engines. A great number of experiments 
on waggons, alone or united in considerable trains, will 
have for their object to show the real value of the friction. 

The resistance of locomotive engines was still an un- 
solved question. We have endeavoured to determine it 
by three different processes, which may serve to verify 
each other. 

The additionol friction created in the engine by the load 
it draws, had never yet been submitted to any investiga- 
tion. We shall present numerous experiments on that 
subject. 

The exact determination of the pressure of the steam in 
the cylinder, was necessary to explain the mode of action 
of locomotive engines, as well as that of steam engines in 
general, and to calculate the work they can perform in 
different circumstances. The erroneous ideas admitted in 
that respect, were the origin of all the faulty calculations, 
which experiment contradicted. We trust that the simple 
elucidation of that point wiU in a manner lay open the 
whole play of the engine. 

The evaporating power of the engines was an element 
on which no experiment had yet been made, which was 
not even introduced in the calculations, and on which> 
however, definitively depends the effect these engines are 
able to produce. Experiments made on that subject, 
upon a great number of engines, will be found in this 

work. 

An analytical equation, that might be adapted to solve 



TO THB FIRST EDITION. IX 

the general problem of locomotive engines, was entirely 
wanting; that is to say, an equation by which might be 
known i priori, either the effects resulting from the given 
proportions of an engine, or, vice versd, the proportions 
that ought to be adopted, in order tiiat predetermined 
effects in regard to load or speed may be obtained. The 
trials hitherto made to come to a solution of this question, 
being founded on a false principle, had produced formulas 
in evident contradiction with facts. A rule had even been 
adopted, according to which the practical power of an 
engine was considered as equal to the third part only of 
its calculated or theoretical power; whereas, the whole 
applied power must evidentiy appear in the effect pro- 
duced, and we shall see that it really does appear in it* 
This imaginary rule is a sufficient proof of the error of the 
calculations that were used, and could only lead to dis- 
appointments in practical applications. Engines were 
constructed, but the effect that they would produce was 
unknown. By the introduction of a new element of cal- 
culation, wrongly neglected imtil now, viz. the vaporizing 
power of the engines, it will be seen, that that question is 
solved in the most simple manner possible. From that 
equation, and simply by measures taken on the machine, 
the velocity and load of a locomotive epgine may be 
immediately found, and vice versa, the proportions which 
ought to be given to it, to make it answer any intended 
purpose. A great number of experiments, made in a 
daily practice, will show the accuracy of the formulae. 
This is, at the same time, the theory of all high-pressure 
steam engines. 

Several secondary dispositions of the mechanism of the 



X INTRODUCTION 

engines had not yet been studied. It will, however, be 
seen that they are apt to deprive the machine, in certain 
circumstances, of as much as a fourth part of its power. 
The effects of these dispositions, and in particular of that 
which is called the lead of the slidCy will be submitted to 
calculation, and the results verified by special experiments. 

The resistance proper to the curves of the railway 
deserved also to fix our attention. We shall endeavour to 
fix accurately the form of the wheels, and the disposition 
of the rails, by which that resistance may most effectually 
be remedied. 

The consumption of fuel according to the load had not 
been determined in a satisfactory manner, and the rule 
proposed was contradicted by the experiment. This 
question wUl be established in a different manner, and 
the results confirmed by facts. 

The researches on those points were made on twelve 
different engines, and numerous experiments were imder- 
taken on each branch of the subject. 

The method constantly followed consists in taking, first, 
the primary elements of the question from direct experi- 
ment; then making use of those elements to establish a 
calculation in conformity with theoretical principles ; and, 
lastiy, submitting the results to fresh and special experi- 
ments, in order to obtain their verification. For the 
furtiier elucidation of the formulee, they are each time care- 
fully submitted to particidar applications; and, finally, 
to extend the use of the work to persons who may wish 
to find the results without calculations, the formul® are 
followed by practical Tables, suitable to tiie cases which 
occur the most frequentiy in practice. 



TO THE FIRST EDITION. XI 

It does not enter into the plan we have traced our- 
selves^ to give an elaborate description of the engine, nor 
the measures of its different parts, except those necessary 
for the researches we undertake. Such considerations 
would lead us too far, and concern more particularly works 
on construction. In like manner, the figures of the Plates 
added to our work are only meant as illustrations of the 
text. They would be too imperfect for any other object. 

The untrodden path in which we have been forced to 
enter, may have led us into some error. We by no 
means pretend to have produced a perfect work, and we 
claim indulgence for the mistakes which may have escaped 
us in so new a subject. Our chief aim was to be 
useful, while seeking a study congenial to our taste, and 
occupying the leisure of an inactive life. Early devoted 
to other pursuits, belonging to a flEUDaily for several gene- 
rations engaged in the military career, and the son of 
a General of Artillery, whose footsteps had naturally 
traced our direction, our studies would not have taken 
that turn, had we not been struck by the powerful effects 
of the moter we are going to describe, and by the im- 
portant pait it must necessarily act in modem civilisation. 
We thought our work would at least have this result, to 
call the public attention to the subject. We shall feel 
happy if we have succeeded in some of our researches; 
and happy also if others, in correcting our errors, shall 
at least elucidate the facts upon which we have called their 
attention. 

All the experiments related in the work were made by 
ourselves, witii all tiie care and attention they required. 
Some were made in company with engineers of known 



XU INTRODUCTION 

talent and ability, as Mr. J. Locke, of the Grand-Junction 
Railway, and Mr. King, of the Liverpool Oas Works. 
We give them in all their details, with a view that every 
one may judge of their accuracy; and we mention the 
place and date of each experiment, in order to facilitate 
their verification by referring to the books, in which is 
re^tered the weight of each of the trains. 

In regard to the fecility we had of making these nu- 
merous experiments, we must say that, having applied to 
the heads of the most important concerns of the sort in 
England, we were permitted, without restilction, to pene- 
trate into the workshops, to take every measure, to collect 
all the documents concerning the expenses, and, lasdy, to 
make any experiment that appeared necessary to us. 

It is with pleasure we acknowledge in the English 
character the liberality we have found in the whole course 
of our investigations. 

To the friendship of Mr. Hardman Earle, one of the 
Directors of the Liverpool and Manchester Railway, we 
owe in particular our warmest thanks. His obligingness 
never abated. Possessing all the qualities of an enlight- 
ened mind, he liked taking a part in researches which 
appeared to him conducive to the progress of science; 
and he permitted us to use all the engines and waggons of 
the railway. The beauty of these engines, their number, 
which is not less than thirty, the care with which they are 
kept, and the immense trade on that line, which gives the 
facility, without interfering with the business of the rail- 
way, to select loads for experiments as considerable and 
as light as one wishes, make that place the only one, 
perhaps, in the world, where experiments on a great scale 



TO THE FIRST EDITION. XIU 

may be made with the same precision as in general can 
only be obtained by a small apparatus. It is for that 
reason we preferred that railway to any other at present 
in activity, either in f*rance or in England. 

The same facilities were also offered us by the Directors 
of the Stockton and Darlington Railway. Interesting 
documents concerning the repairs and expenses of all 
sorts^ incurred by that Company, were obligingly com- 
municated to us. We owe that obligation to the liberal 
authoris&ation of Mr. J. Pease, M.P., Chairman of the 
Company, and to the unremitting attentions of Mr. Robert 
B. Dockray. 

We have studied the subject with all the interest, and, 
we might say, with all the enthusiasm it excited in us. In 
fact, what a subject for admiration is such a triumph of 
human intelligence ! What an imposing sight is a locomo- 
tive engine, moving without effort, with a train of 40 or 50 
loaded carriages, each weighing more than ten thousand 
pounds! What are henceforth the heaviest loads, with 
machines able to move such enormous weights ? What are 
distances, with moters which daily travel 30 miles in an 
hour and a half? The ground disappears, in a manner, 
under your eyes; trees, houses, hiUs, are carried away 
from you with the rapidity of an arrow; and when you 
happen to cross another train travelling with the same 
velocity, it seems in one and the same moment to dawn, 
to approach, and to touch you; and scarcely have you 
seen it with dismay pass before your eyes, when already 
it is again become like a speck disappearing at the 
horizon. 

On the other hand, how encouraging is the evident 



/ 
XIV INTRODUCTION TO THE FIRST EDITION. 

prosperity of those fine establishments ! How satisfactory 
it is to acquire the proof that the Liverpool and Man- 
chester Railway produces 9 per cent, interest, and the 
Stockton and Darlington an equal profit! With what 
confidence must we not anticipate the future state of such 
undertakings, when we know that, besides the above- 
mentipned annual interest, the shares of the Liverpool 
Railway have risen, in four years,' from £100 to £210; 
and those of the Darlington Railway, in eight years, from 
£100 to £300 ? What may not society at large expect in 
future from this new industry, which will augment, ten- 
fold, the capital and produce of the country, by the 
immense influence of speedy and economical conveyance ! 
It is then with the liveliest wish to see this new branch 
of industry difiused as it merits, that we have undertaken 
the work which we now present to the public. 

^ The first edition of this work appeared in French, in the 
beginning of 1835. 



INTRODUCTION 

TO THE SECOND EDITION. 



The Introduction to the first edition, which is here 
reprinted such as it was published in 18B5, exposes the 
plan we had proposed to ourselves in this work, and the 
facilities that were afforded us for studying the subject. 
But as a first essay necessarily falls short of what is to be 
desired, we have since devoted ourselves to new re- 
searches, to endeavour, as fieur as in us lies, to supply the 
deficiencies which at first we could only indicate. 

This task we began in the month of August, 1836, as 
will be seen by the dates of the experiments which will be 
presented in the work. Unable, at the period of our first 
edition, to find a satisfactory means of separating, in our 
experiments, the resistance of the air against the trains, 
from the friction proper to the waggons, we were con- 
strained to take account of that resistance at an average 
velocity of 12 to 15 miles per hour, leaving it imited to 
the friction of the waggons, tiiat is to say, giving a valu- 
ation of those two resistances together at that velocity. 
But recognising the want of a more precise determination 
of the special value of each of those two resistances, we 



XVI INTRODUCTION 

undertook^ in the month of August, 1836, on the Liverpool 
and Manchester Railway, a series of experiments on the 
subject, and published the results of them, blended with 
other matters, in a series of papers printed in the donates 
reridus of the sittings of the Academy of Sciences of the 
French Institut of 1837. And indeed we were not a 
little surprised to find in 1839, in the proceedings of the 
British Association for the Promotion of Science, a long 
article by an English Professor, who, without noticing 
these ulterior researches, indulged himself with the satis- 
faction of pointing out to us an omission already published 
by ourselves, and remedied long since ; and who, in fine, 
proposed a new valuation of the resistance of the trains, 
according to which, far from separating the resistance 
of the air from the friction of the waggons, he pretended 
on the contrary that tiie separation was impossible in the 
present state of science on the subject. 

The experiments which we undertook at the same 
period on the Liverpool and Manchester Railway, com- 
prise also several other researches, such as the pressure 
against the piston caused by the action of the blast-pipe, 
the vaporization of boilers in different circumstances of 
rest and of motion, the effects of a different proportion 
between the fire-box and the tubes, on the total vapor- 
ization of the engine, and on its consumption of fuel, &c. 
The results of the greater part of tiiese experiments have 
been communicated separately to the Academy of Sciences, 
in tiie course of the years 1838, 1839, and 1840, and 
printed in the Comptes rendus ; but they are now collected 
in this edition^ and so arranged, as to complete as much as 
possible the data already offered on locomotive engines. 



TO THB SECOND BDITION. JCVU 

We could have wished all these researdies to be quite 
copclusive; but we do not dissemble that many among 
them are as yet but very incomplete^ that they require 
further study and more varied observations. Such^ how- 
ever, as they are, we yet think them capable of leading 
to useful results; and, at all events, they will have the 
advantage of pointing out the road to. other experimenters 
on the same subjects. We shall be among the first to 
receive with eagerness the new lights which their labours 
may elicit. 

The publication of another work, the subject of which 
appeared to us to be very important, the Theory of the 

Steam Enffine, prevented us, till now, firom bringing out the 

• 

second edition of the TVeatiee an Locomotive Enginee^ 
though the first had long been out of print. The adoption, 
by a great number of authors and engineers,^ at the theory 
and experimental determinations contained in At first 
edition, and the re-production of the work in England, in 
America, and in Germany, seem to us an ample reward 
for all the application and- labour it has cost us. But as 
some authors, in rendering an account of our researches, 

' In France, M. Navier, member of the Jnstitut; in England, 
Professor Whewell, of the Royal Sooietj of London, in the fifth 
edition of his Dreatite on Meckatda; in Prussia, M. Crelle, of the 
Boyal Sodety of Sciences of Berlin, &c., have adopted these re- 
searches ; and in the third edition of his work on Railways, London, 
1838, Mr. Nicholas Wood has inserted, in detail, not only all the 
ezperpiental determinations of the Treatise on Locomotive Engines, 
but even the theory of that engine developed in the same work, 
acknowledging, in a slip expressly added at the head of that 
I, the source from which he took <that theory. 

b 



XVm INTRODUCTION 

have given a mistaken analysis of them^ or have drawn 
from them consequences which we cannot admit, we 
deem it necessary to enter into some details on this 
subject. 

In the edition published in 1838, by Mr. Woolhouse, 
of Tredgold^s work on the Steam Engine, page 186 of the 
Appendix, the editor, wishing to give a succinct analysis of 
our Theory of the Steam Engitie, the same as will be 
found developed in Chapter XII. of this work, but spe- 
cially applied to locomotive engines, says that our theory 
'' may be briefly explained thus : if the evaporating power 
of the boiler be capable of supplying a greater quantity of 
steam, at the required pressure, than is consumed at the 
successive strokes of the piston, it is evident that the 
pressure of the steam in the boiler will gradually increase, 
provided no portion is supposed to escape through the 
safety-valve or otherwise. This increasing pressure will 
gradually accelerate the velocity; and finally, when the 
engine attains her permanent speed, the quantity of steam 
consumed in the cylinder and suj^lied through the steam- 
pipe, must evidently correspond with the quantity eva- 
porated by the boiler. Thus the author pretends to 
introduce a new element into the calculation^ viz., the 
evaporating power of the boiler, which again is to be 
estimated by the quantity of fire surface ; and, the density 
of steam at a given temperature being, according to the 
law of Boyle and Mariotte, proportional to the pressure 
and inversely as the volume, as in the case of gases, the 
evaporating power is measured by the volume of steam, 
generated in a given time, multiplied into its pressure. 
Such a mode of proceeding,'^ continues Mr. Woolhouse, 



TO THB 8ECOXD EDITION. XIX 

'^' does not involve any new doctrine or any principle that 
had not been laid down by Tredgold in the first edition of 
his work.'' 

If oar theory were really represented by this analysis, 
we might perhaps agree that it would offer but little differ- 
ence to that of Tredgold; but on recurring to Chapter 
XII. of this edition, and more especially to our work On 
the Theory of the Steam Engine^ in which the differences 
between the old theory and our own are pointed out in 
detail, and for the divers kinds of steam engines, it will 
be at once recognised that this pretended explanation 
cannot give the slightest idea of our theory ; that a most 
important principle in it consists in the determination of 
the pressure of the steam in the cylinder and its intro- 
duction in the equations, a point which is not even alluded 
to in the foregoing explanation ; that the old theory, by 
coefficients or such as is used by Tredgold, can lead only 
to errors; that it gives the load of the engine inde- 
pendentiy of the velocity of the piston, supporting there- 
fore that tiie engine will always move the same load at 
any velocity ; that it gives the vaporization for a known 
load and velocity, independentiy of the load, so that a 
greater load would not require a greater vaporization; 
that it affords no means of calculating the velocity of an 
engine with a given load ; while our own gives, without 
the least difficulty, the means of calculating the velocity, 
and also the load and vaporization, in accordance with 
the facts and principles ; that in applying the two theories 
to the same engine, the results are so widely different 
that, in some cases, the old theory gives twice or three 
times the result of our own, as will be seen in the work 



XX INTRODUCTIOX 

alluded to ; that our theory explains completely the effects 
of the atmospheric engine, which could not be calculated, 
and those of the Cornish engines, which were so un- 
accountable in the old theory, that the effects related to 
have been produced by those engines, were reckoned 
completely false by many engineers in Great Britain; 
finally, that our theory gives the means of ascertaining 
the velocity, load, expansion and counterweight, which 
produce the maximmn useful effect in a given engine, a 
research which ^m^ totally impossible and even inadmis- 
sible in the old theory. AU these differences have 
escaped Mr. Woolhouse, but they seem to have been 
noticed by the engineers of the Corps Royal des Fonts et 
Chauss^s, in France, who, in 1839, voted a gold medal 
to the theory objected to by Mr. Woolhouse. We there- 
fore refer this author to a more attentive perusal of the 
work which he criticises. 

There has also i^peared in the AtheneBum^ on the 
sitbject of the TTieary qf the Steam Engine^ an anony- 
mous paper, on which we cannot help saying a word. 
The author of this paper, who, whatever he may say to 
the contrary, possesses but a very superficial knowledge of 
these matters, afiirms it to be heedless to undertake new 
inquiries on the steam engine, since he knows all that 
is to be known on the subject. He even deems it 
^* absurd ^^ to attempt to ground the calculation of the 
eflect of steam en^es on the production of steam in their 
boiler ! A writer whose ideas on this subject are so clear 
and so profound, has indeed a right to cut questions 
short, and set himself up as defender of British en- 
gineers, whom he declares to be attacked in their honour. 



TO THfl 8BCOKD BDITION. XZl 

by the very £act of new inquiries on the subject of the 
steam engine. With such feelings as these^ the most 
foreign to tnie science^ the article is written. As beyond 
this, however, the author enters into no scientific discus* 
sion, and as, too diffident to take on himself the respon- 
sibility of his own judgments, he rests modestly under 
the shelter of his incognito, and has even carried the 
anonymous system so fieur as to make in public, to the 
author whom he has attacked in secret, demonstrations of 
esteem, the motives of which all may appreciate at their 
real value, we think ourselves excused from stopping to 
answer him any further. 

Finally, Mr. Josiah Parkes has just published, in the 
Transactions of the Insiitution of CwU Engineers of Lon- 
don, voL iii., a long paper in which he undertakes the 
determination of a coefficient or numerical relation, repre- 
senting in mass all the divers resistances which locomotive 
engines have tm overcome in their motion, so as to render 
useless all separate research, relative to the value of fric- 
tion, resistance of the air, &c. With this view he enters 
into a long discussion on the experiments of the Treatise 
on Locomotive Engines, and on all the experiments on the 
same subject published by divers en^eers; and to de- 
monstrate the difficulties insurmountable, in his opinion, 
and the uncertainty, attending researches of this kind, he 
indicates divers verifications which, as he says, these 
experiments ought to satisfy. As the author gives on the 
subject a great number of arithmetical calculations, the 
errors of whidi might not be perceived at a first glance, 
we shall here enter, with some detail, into the examination 
of his pretended verifications. 



\ 



XXU INTRODUCTION 

On seeing thejundamental errors on which his reasoning 
and his calculations are grounded, the inaccuracy of the 
results at which he has arrived will at once be recognised. 

1st. Mr. Parkes proposes to calculate the pressure at 
which the steam was necessarily expended in the cylinder 
of each engine submitted to experiment, in order after- 
wards to compare that pressure with the pressure resulting 
from the totality of the divers determinations of resistances 
exerted against the piston, according to the Treatise on 
Locomotive Engines. With this view, he seeks, from the 
velocity of the engine, the number of cylinders-full of 
steam which were expended per minute. Comparing the 
volume thus obtained to the volume of water vaporized in 
the boiler, he concludes the relative volume of the steam 
during its passage into the cylinder ; and finally, recurring 
to the Table of the relative volumes of steam under diveiis 
pressures, contained in the Theory of the Steam Engine^ he 
concludes the pressure which the steam must necessarily 
have had. This is conformable to the theory developed 
in the Treatise on Locomotive Engines, which, in fact, Mr. 
Parkes entirely adopts. But to perform this calculation, 
Mr. Parkes takes the average velocity of the whole trip 
from Liverpool to Manchester, and from that velocity he 
pretends to deduce the mean pressure in the cylinder 
during the same trip. Now it will be easy to prove by 
an example that this mode is altogether faulty. 

Suppose, in effect, the engine Atlas have travelled a 
distance of 30 mUes in an hour and a half, vaporizing 60 
cubic feet of water per hour. As the wheel of the engine 
is 5 feet in diameter, or 15*71 feet in circumference, as 
there are two double cylinders-full of steam expended at 



TO THE SECOND EDITION. XZlll 

every turn of the wheel, and as the capacity of those two 
double cylinders, including the filling-up of the steam-ways, 
amounts to 4*398 cubic feet, it follows that the volume of 
the steam which passes into the cylinders per mile per- 
formed, or per distance of 5280 feet, is — —- x 4*398 

^ ' 15-71 

= 1478 cubic feet. 

This premised, when Mr. Parkes refers to the average 

velocity of the whole trip, to value the pressure in the 

cylinder, as that velocity was 20 miles per hour, and as 

the vaporization at the same time was 60 cubic feet of 

water per hour, he finds for the ratio of the volume of 

1478 X 20 
the steam expended to the volume of water, — 

^ 60 

=492*7. And consequently, riecurring to the Table of the 

relative volumes of steam under different pressures, he 
obtains for the corresponding total pressure 56*66 lbs. 
per square inch ; and, deducting the atmospheric pressure, 
he obtains for the effective pressure, 41*95 lbs. per square 
inch. 

But to show that this mode of calculating, from the 
average velocity, can only lead to error, let us suppose that, 
by reason of the divers inclinations of the portions of the 
railway, the first 15 miles have been traversed in half an 
hour, and the other 15 miles in an hour, which still makes 
30 miles in an hour and a half; as 30 cubic feet of water will 
have been vaporized in the first half hour, or during the pas- 
sage of the first 15 miles, and 60 cubic feet of water during 
the next hour, or in the passage of the last 15 miles, it is 
plain that the volume of the steam will have been respec- 
tively in each of those times, — ^ — ^ .= 7^9, first, and 

30 



XXIT INTRODUCTION 

afterwards ' ^ = 369*5 . Whence restdts. accord-' 

60 ' 

ing to the Table, that the effective pressure of the steam 

will have been successively 21*62 and 62-95 lbs. per square 

inch. 

Thus^ during the first half hour the effective pressure 

will have been 21*62 ; during the second half hour it will 

have been 62*95, and during the third again 62*95. Con- 

sequently, taking account of the time during which the 

pressure has had these respective values, it is plain that 

the mean effective pressure in the cylinder will really have 

1 _ 21*62 + 62*95 + 62*95 _ .^.i ^^ _ • i, 

been ■ ■ =s 49*1/ ms, per square mch, 

and not 41*95 lbs. per square inch, as it is given in Mr. 
Parkes^s calculation ; which, by the fact, supposes all the 
portions of the trip to have been performed in equal times. 
In this case, therefore, which has nothing in it but what 
is very ordinary, there would be an error of 7*22 lbs. per 
square inch out of 41*95 ; that is, an error of more than -^ 
on the effective pressure of the steam. It is evident that 
the calculation, such as Mr. Parkes makes it, is exact only 
for portions of road composed of one inclination or tra- 
velled with uniform velocity, and that it cannot apply to 
the total passage of a line composed of different incli- 
nations. For further elucidations on this head we refer 
to Chap. XVII. of this work, relative to inclined planes, 
and to Chap. XII., in which all the experiments con- 
sidered by Mr. Parkes are calculated. 

2nd. We have just shown a first error which Mr. Parkes 
introduces, as a fundamental basis, in his calculation of 
the pressure of the steam in the cylinder. But he does not 



TO THB 8BCOND EDITION. ZXT 

» 

stop there. In the Table of experiments on the yaporisar 
tion of the engines (Chap. V. Art. IV. § 1 of the Treatiie 
Oft Locomotive Engines, 1st edition^ and page 258 in this)^ 
we have given the average velocity of the engines during 
each trip ; and that velocity is obtained simply by dividing 
the whole distance performed by the time employed in 
performing it^ as is seen in the Table in question. It would 
be natural then for Mr. Parkes^ who, as has been said 
above, is satisfied with average velocities in his calcula- 
tions, to take those which are given in the Table ; but in* 
stead of that, he augments almost aU the velocities about i^ 
Thus, for instance, the Vulcan, which travelled 29*5 
miles in 1 hour 17 minutes, and whose average velocity in 
consequence appeared to be 22*99 miles per hour, had, 
according to him, a velocity of 26*90 miles per hour. The 
velocity of the Vbsta rises from 27*23 to 31*60 miles per 
hour, and so of the others. The critic falls into this new 
error because, in the Treatise on Locomotive Engines, 
(Chap. IX. § 2, 1st edition, and p. 311 in this), in 
speaking of fuel, it is said that, when the engines ascend 
without help the inclined planes of the Liverpool and 
Manchester Railway, the surplus of work, thence result- 
ing for them, equals, on an average, the conveying of ' 
their load to -j- more of distance, and Mr. Parkes logically 
concludes from this that the velocity of the engine must 
be by so much increased. So that if an engine perform 
1 mile in 4 minutes, ascending a plane inclined -J^, 
which renders nearly five-fold the work of the engine, 
it would follow, from this calculation, that the velocity 
would not have been 15 miles per hour, but 15 x 5 = 75 
utiles per hour, since the quantity of work done would 



XXVI INTRODUCTION 

have been five-fold ! Mr. Parkes's' error proceeds from 
his having applied to the velocity a correction which 
belongs only to the work done, and, as a consequence, to 
the/iieL 

But on examining what effect results from this substi- 
tution of the imagined velocity of Mr. Parkes for the 
observed velocity, it will be remarked, that whenever an 
engine is obliged to ascend without help one of the in- 
clined planes of the Liverpool and Manchester Railway, it 
exerts in that moment, as we have said, an effort about 
five times as great as upon a level, and draws its load less 
rapidly. One would deem it then allowable to conclude 
that the average pressure of the steam in the cylinder 
must be augmented, since, during a certain portion of the 
trip, tiie effort is greater, and that the useful effect per unit 
of time must be diminished, since during the same time 
the useful load is drawn at less velocity. But no. Mr. 
Parkes's calculation, by augmenting the apparent velocity 
of the engine, demonstrates that, in this case, the average 
pressure in the cylinder becomes on the contrary much 
less and that the useful effect becomes much greater. So 
that the error committed produces itself here in the two 
opposite ways. 

With these elements Mr. Parkes establishes the whole 
of his calculations and of his Tables, to the very end of his 
paper; and as, to augment the evil, this pretended correc- 
tion happens to be made on one portion of the experi- 
ments, without being made on the rest, there results an 
inexplicable confusion in all the calculations. Thus also 
it happens that his determinations of the horse-power pro- 
duced per cubic foot of water vaporized, or of the quan- 



TO THE SECOND EDITION. XXVU 

tify of water employed to produce the power of one 
horse, and all the consequences thence deriyed, are in 
every way erroneous. 

3rd. After having thus calculated very exactly the pres- 
sure of the steam in the cylinder, Mr. Parkes compares 
the result which he has obtained, with the total pressure 
on the piston resulting from the partial resistances suffered 
by the engine, according to the Treatise on Locomotive 
Engines; and as, in the first edition of the work, the 
author had confined himself to mentioning the pressure 
against the piston due to the action of the blast-pipe, 
without making any experimental research on the subject, 
Mr. Parkes takes the difierence between the two results, 
as necessarily expressing the pressure due to the blast- 
pipe ; and he demonstrates the inaccuracy of it. Here 
we perfectly agree with him; for, besides the errors 
already pointed out in his research of the pressure of the 
steam in the cylinder, every thing variable that can occur 
in the different data of resistance, now passes to the 
account of the pressure due to the blast-pipe, and must 
necessarily come to falsify the calculation of it. Thus for 
instance, in the experiments made with the Firefly, the 
boiler lost water by the tubes, and there resulted an appa- 
rent vaporissation greater than the true one. A part of the 
difference between the calculated and the observed pres- 
sure was therefore to be attributed to that cause, though it 
could not be accurately measured ; but, by the calculation 
of Mr. Parkes, it all passes to the accoimt of the pressure 
due to the blast-pipe. Similarly, the resistance of the air, 
then imperfectly computed in the total resistance for an 
average velocity of about 12 miles per hour, is found, in all 



XXYIU INTRODUCTION 

cases of greater yelocity, to augment considerably the pres- 
sure due to the blast-pipe^ and on the contrary to diminish 
it in all cases of less velocity. A contrary or a favourable 
wind; waggons well or imperfectly greased, &c*, necessarily 
produce similar effects. Thus circumstances, combined 
with the errors already introduced into the calculation, 
raise or lower that pressure to all imaginable degrees ; and 
it will readily be imagined that such a determination can- 
not be exact. 

4th. Mr. Parkes has observed, in the experiments of 
the Treatise an Locomotive Engines, and particularly in 
two of them, made on the Lbeds engine, and quoted in 
the Theory of the Steam Engine, that the useful effects 
produced by the same quantity of water vaporized varies 
according to different circumstances ; and he is amaaed at 
it; for, as he affirms, the useful effects produced by the 
same quantity of water vaporized, in the same time and 
under the same pressure in the boiler, ought in all cases 
to be identical. But this again is merely an error of the 
critic ; for if we suppose a locomotive engine drawii^ a 
heavy load at a small velocity, since it is only at a small 
velocity that the engine has to overcome its firiction, as well 
as the atmospheric pressure against the piston, and, above 
all, the resistance of the air against the train, it foUovrs that, 
out of the quantity of total work executed, there will be 
but a trifling portion lost in overcoming those resistances ( 
but i^ on the contrary, we suppose the same engine per- 
forming precisely the same quantity of total work, but 
drawing a light load at a great velocity, it is obvious that 
a much greater part of the work done will be absorbed in 
moving, at that velocity, the resistance which represents 



TO THE SECOND EDITION. XXIX 

the friction of the engine, as well as the atmospheric pres- 
sure against the piston, and in overcoming the resistance 
of the air, which increases as the square of the velocity ; 
and consequently there will remain a much smaller por- 
tion of it applied to the producing of the useful effect. 
Hence, in the two cases considered, the useful effects 
produced by the same quantity of water vaporised, so hi 
from being identical, will, on the contrary, be very dif- 
ferent from each other. Mr. Parkes may, besides, satisfy 
himself on this point, by perusing the TTkeory of the Sieam 
Bnffine, in which he will find numerous examples of steam 
engines, in which the useful effect of 1 cubic foot of 
water varies in very wide limits, according to the 
velocity of the motion or the load imposed on the 
engine. Thus Mr. Parkes's reasoning errs again by 
tiie basis itself. 

5tli. But there is another prindple to which Mr. Parkes 
would subject all the observations of vaporiaation of loco- 
motive engines. He remarks that in. the two experiments 
above cited, the total resistance opposed to the motion of 
the fMston is different in the two cases. Consequentiy, 
says he, the quantities of water vaporized by the engine in 
the same time must be in proportion to the pressures 
observed in the cylinder, and the experim^its must satisfy 
this condition. 

To establish this new principle, Mr. Parkes recurs to 
the Treatise on Locomotive Engines itself. He quotes a 
passage in which, supposing the same engine travelling the 
same distance with two different loads, the author says posi- 
tively that the distance travelled being the same* in both 
cases, the number of turns of the wheel, and consequently 



XXX INTRODUCTION 

the number of strokes of the piston given by the engine^ 
that is to say^ the number of cylinders-fdll of steam, or, 
finally, the total volume of steam expended, mil also be the 
same in both cases ; whence results that the same volume 
will successively have been filled with two steams at dif- 
ferent pressures, or, in other words, at difierent densities ; 
and consequently the quantities of water which have 
served to form those slibams will be in proportion to 
their respective pressures (Chap. IX. § 1, 1st edition). 
Thus, this passage establishes very distinctly that the 
quantities of water vaporized, /or the same distance, are in 
proportion to the pressures of the steam in the cylinder. 
But what does Mr. Parkesxx>nclude from this ? Why, that 
the quantities of water vaporized in the same time are in 
proportion to the pressures in the cylinder. Now, it hap- 
pens to be just the contrary ; for if we suppose, by way 
of example, the two pressures to be in the ratio of 2 to 1, 
the volumes of water vaporized for the same distance will 
also be as 2 to 1 ; but if the time employed in performing 
the distance in question be two hours in the first case and 
one hour in the second, it is plainly the quantities of 
water vaporized in two hours and in one hour respectively, 
which will be one to the other in the ratio of 2 to 1> so 
that the vaporizations per hour, or m the same time, will 
be equal instead of being in. the ratio of the pressures. 
Thus it is clear again that Mr. Parkes's principle rests but 
on a new error, which consists in making a confusion be- 
tween the vaporizations for the same distance and the 
vaporizations for the same time. 

6tii. A final observation of Mr. Parkes is this, that in 
some experiments, the locomotive engines produced, for 



TO THE SECOND EDITION. XXXI 

* 

the same quantity of water vaporized^ a greater useful 
effect than several stationary high-pressure steam engines^ 
or even than several condensing steam engines; and 
he considers this result as a proof of the uncertainty 
of those observations; for, says he, the locomotive en- 
gines having to contend with the pressure arising from 
the blast-pipe, which the high-pressure engines have 
not, and also with the atmospheric pressure, neither of 
which resistances the condensing engines have to con- 
tend with, it is incontestable that they cannot even pro- 
duce equal effects, much less superior ones. But this 
reasoning is as unfounded as those we have already 
noticed; for since the useful effect of steam engines for 
the same vaporization, diminishes as the velocity of their 
motion increases, which is found developed, either in the 
present work. Chap. XII., or in the Theory of the Steam 
Engine^ it is easy to conceive that a locomotive, working, 
for instance, at its maximum useful effect, that is to say, 
with its maximum load, and consequently at a very 
small velocity, at which -the pressure due to the blast- 
pipe and the resistance of the air are nearly null, can 
produce a useful effect greater, nay much greater than a 
stationary high-pressure engine, working on the contrary 
with a light load and a great velocity. The same in- 
feriority of effect, relative to a locomotive, may also occur 
in a condensing engine, because an engine of that system, 
working, for instance, at 16 lbs. pressure 'per square inch 
in the cylinder, and condensing the steam to 4 lbs. per 
square inch under the piston, where the pressure is always 
greater than in the condenser, loses, by that fact alone, a 



XXXU INTRODUCTIOX 

quarter of the power that it applies; whereas a loco- 
motive working at 5 atmospheres in the cylinder, and at 
a very small velocity, which renders almost null the pres- 
sure due to the blast-pipe, suffers, by the opposition of 
the atmospheric pressure, a loss equal to but -^ of its total 
power. Hence, definitively, in the latter engine, the 
counter-pressure against the piston destroys a smaller 
portion of the total power applied, and consequently, 
without even noticing the difference of the friction of the 
two engines, or entering into any other consideration 
relative to the velocity, it is conceivable that tiie useful 
effect of tiie locomotive may be found the greater. 

But if a more complete procrf be desired, it will be 
easy to furnish it; for the relative volume of the steam at 
16 lbs. per square inch, being 1672 times that of the water, 
it is plain that if S represent the number of cubic feet of 
water vaporized per minute in the boiler, and if a represent 
the area of the cylinder expressed in square feet, 1672 S 
will be tiie volume of the steam generated per minute, 

16*72 R 

whence results that — t will be the velocity assumed 

a 

by the piston of the engine working at that pressure. 
Moreover, the ej^ective pressure of the steam or the load 
which the piston can support, i8l6 — 4 = 12 lbs. per square 
inch ; which gives 12 x 144 a for the total resistance sup- 
ported by the piston. Thus, in the condensing engine, 
the effect produced by the number S of cubic feet of water, 
is expressed by 1672 x 12 x 144 S = 20064 x 144 S. Cal- 
culating in the same manner the case of the locomotive 
engine, we find that the effect it produces for the same 



TO THE SECOND EDITION. XXXIU 

vaporization S, working at the total pressure of 7^ I&s. per 
square inch, or at the effective pressure of 60 lbs. per 
square inch, is 381 x 60 x 144 S = 22860 x 144 S. There- 
fore, finally, its useful effect, per cubic foot of water 
vaporized, will exceed that of the condensing engine, and 
this again is a circumstance, examples of which will be 
found in the Theory of the Steam Engine, 

Thus this new peremptory condition which the experi- 
ments ought to satisfy is as unfounded as the former ones. 
It will be remembered, besides, that the velocities em- 
ployed by Mr. Parkes, for locomotive engines, being nearly 
all considerably augmented, as has been explained above, 
he must necessarily arrive at exaggerated results, for the 
effects which he supposes to have been produced by those 
engines. 

It is remarkable, finally, that in applying the preceding 
considerations to aU the experiments published on loco- 
motives by different engineers, namely : Messrs. R. Ste- 
phenson, N. Wood, E. Wood, and Lardner, Mr. Parkea 
finds that the conditions to which he proposes to subject 
those experiments are not verified in them. Such a result 
ought to have put him on his guard against the validity of 
his own arguments: but the want of using equations, 
which facilitate so much accuracy in mathematical reason- 
ing (and the author accounts for it in telling us that he is 
more accustomed to handle the hammer than the pen), 
causes him to heap errors on errors, combining and 
complicating them unaware, till he arrives at a point 
where he does not produce a single result that is not 
erroneous. 



XXXIV INTRODUCTION 

There is matter of surprise in the numberless errors 
contained in the paper of Mr. Parkes^ and of which we 
have noticed merely the principal ones ; but on inquiring 
what was the end he had proposed to himself^ what was to 
be the definite consequence of his labour, one is yet much 
more surprised. Collecting all the erroneous results which 
he has obtained, Mr. Parkes forms a Table in which he 
sets in view, on one side, the vaporization effected by the 
engine, and on the other side, the useful and the gross 
effect produced ; but to the latter he gives the name of 
momentum* Then, comparing the vaporization to the 
effect produced, and taking an average upon all the ex- 
periments which he has collected from all the works pub- 
lished on the subject, he presents, as the result of his 
labours, the following conclusion, which he proposes to 
substitute in place of every other kind of research on 
locomotive engines. 

When the velocity of a locomotive engine is augmented 
^n the proportion of 1*52 to 1, the vaporization necessary 
to produce the same effects varies in the following pro- 
portions : 

To produce the same momentum (the same gross effect, 
weight of waggons and engine included), in the proportion 
of 1*42 to 1, or in a proportion something less than that 
of the velocities; to produce the same commercial gross 
effect (the same gross effect including the weight of the 
waggons), iu the proportion of 2*43 to 1, or nearly as the 
squares of the velocities ; to produce the same useful effect, 
in the proportion of 3*11 to 1, or nearly as the cubes of 
the velocities. 



TO THE SECOND EDITION. XXXV 

This is the definitive result which Mr. Parkes has 
attained^ and the help of which seems to him to render it 
needless henceforward to seek to determine either the 
friction of the waggons^ or that of the engines, or the 
resistance of the ur, or any thing in fact thift may in- 
fluence the effects produced ; researches which itppear to 
him to offer insurmountable difficulties. Possessed of the 
wholesale result of Mr. Parkes, nothing more will be 
needed. Does any one wish, for instance, to know what 
load a given engine will draw at 25 miles per hour on a 
given inclination ? to know what velocity it will assume 
with a load of 60 tons ? to know what is the maximum of 
useful effect that it is capable of producing? to know 
what proportions must be given to it, in order to ob- 
tain desired effects? Why, having recourse to Mr. 
Parkes's result, the solution of all these questions is 
self-evident ! 

It is evident, on the contrary, that Mr. Parkes's rule, 
even were it exact instead of being founded on erroneous 
calculations, could lead to but one thing, namely, that of 
finding the gross or useful effect produced by an engine at 
the velocity of 30 miles per hour, when the same effect is 
known at the velocity of 20 miles. But, even then, 
making use of so rough an approximation, in which all is 
thrown in the lump : friction of the waggons, friction of the 
engine, resistance of the air, resistance owing to the blast- 
pipe, &c., the result could never be depended on. As- 
suredly, calculations like these do not tend to the progress 
of science ; they would rather lead it back again to its first 
rudiments. For this reason we persist in our belief that 
the only means of calculating locomotive engines, is to 



XXXVl INTRODUCTION TO THB SECOND EDITION. 

endeavour to determine^ as exactly as possible, each of the 
resistances which oppose their motion, and by taking 
account of the value of each of those forces in the calcxila- 
tion, we may in every case attain a valuation really 
founded m principle, of the effects of every kind that are 
to be expected from them. 



C ONTENTS 



Introduction to tbb First Edition 
Introduction to thb Second Edition 



TAQM 
V 

zv 



CHAPTER I. 



DESCRIPTION OF A LOCOMOTIVB BNGINB. 



Article I. Detail and disposition of the parts. 

Sect. I. Of the Boiler 

Sect. II. Of the action of the Cylinders 

Sect, iii^ Of the Cranks and Wheels 

Sect. IV. Of the Safety-valves . 

Sect. Y. Of the Water-Gange 

Sect. VI. Of the Slides 

Sect. VII. Of the Eccentric Motion 

Sect. VIII. Of the Drivers 

Sect. iz. Of the Pumps 

Sect. z. Of the Regulator 

Sect. zi. Of the joints or rubbing parts 

Sect. zii. Of the Fire-grate 

Sect. ziii. Of the disposition of the different 



parts 



1 
8 
9 
12 
13 
14 
16 
20 
25 
26 
27 
27 
28 



XXXVIU CONTENTS. 



Articlb II. 0/ the principal dimensions of the Engines. 



PACK 



Sect. I. Of the dimensions of the parts from which 

the power of the engine is derived . 33 

Sect. II. Dimensions of the fire-hox and boiler of 
some of the best locomotive engines 
of the Liverpool and Manchester 
Railway ..... 35 

Sect. III. Of the old locomotive engines . . 38 



CHAPTER II. 

OP THB LAWS WHICH RKOULATS THI MECHANICAL ACTION OP 

THB 8TKAM. 



Sect. I. Relation between the temperature and 
the pressure of the steam in contact 
with the liquid . . . .41 

Sect. II. Relation between the relative volumes and 
the pressures, at equal temperature, or 
between the relative volumes and the 
temperatures, at equal pressure, in the 
steam separated from the liquid 53 

Sect. III. Relation between the relative volumes, the 
pressures, and the temperatures, in the 
steam in contact or not in contact with 

the liquid 56 

Table of the temperature and volume of 
the steam generated under different 
pressures, compared to the volume of 
the water that has produced it 60 



CONTENTS. XXXIX 

PAGE 

Sect. IV. Direct relation between the relative vo- 
lumes and the pressures, in the steam 
in contact with the liquid . 61 

Sect. V. Of the constituent heat of the steam in 

contact with the liquid ... 65 

Sect. VI. Of the conservation of the maximum den- 
sity of the steam for its temperature, 
during its action in the engine 71 



CHAPTER III. 



OF THB PRB8SUBK OF THE STB AM, IN LOCOMOTIVB BNGINB8. 



Articlb I. Of the safety-valves. 

Sect. I. Of the pressure calculated according to the 

levers and the spring-balance . 82 

Sect. II. Of the corrections to be made to the weight 

marked by the spring-balance . 87 



Articlb II. Of the instruments specially destined to measure 

the pressure. 

Sect. I. Of the barometer-gauge, or syphon- 
manometer ..... 92 
Sect. II. Of the air-gauge .... 102 

Sect. HI. Of the thermometer-gauge . . .109 
Sect.- IV. Of the spring-gauge, or indicator 111 

Sect. V. Comparative Table of the divers modes of 

expressing the pressure .113 



Xl CONTENTS. 



rxcB 



CHAPTER IV. 



OP THB RR8I8TANCB OF THB AIR. 



Sect. I. Of the intensity of that resistance on the 

unit of surface . . . 1 14 

Sect. II. Of the resistance of the air against the 

waggons, isolated or united in trains . 120 

Sect. III. Table of the resistance of the^air against 

the trains 131 



CHAPTER V. 

ON THR FRICTION OF THR WAGGONS ON RAILWAYS. 

Sect. I. Necessity of new inquiries on this subject 135 
Sect. II. Of the friction of waggons determined by 

the dynamometer . . .137 

Sect. III. Of the friction of carriages, determined by 
the circumstances of their spontaneous 
descent and stop upq^ two consecutive 
inclined planes . .139 

Sect. IV. Experiments on the friction of waggons . 153 
Sect. V. Of the causes of variation in the friction 

of carriages 164 



CHAPTER VI. 

OF GRAVITY ON INCLINED PLANBS .168 



CONTENTS. Xli 

PAOB 

CHAPTER VII. 

OP THB PIIB88UER PRODUCBD ON THB PISTON BT THB ACTION OP 

THB BliABT-PIPB. 

Sect. I. Of the effects of the blast-pipe . .174 
Sect. II. Experiments on the resistance produced 
against the piston by the action of the 
blast-pipe . . - . . 182 
Practical Table of the pressifres against the 
piston, due to the action of the blast- 
pipe 198 

CHAPTER VIII. 

OP THB PRICTION OP LOCOMOTIVB BN0INB8. 

Articlb I. Of the friction of unloaded locomoHve engines. 

Sect. 1. Of the divers elements of the friction of 

locomotive engines 200 

Sect. II. Of the different modes of determining 
the friction of miloaded locomotive 
engines 203 

Sect. III. Friction of the engines, determined by the 
smallest pressure of steam necessary to 
keep them in motion 205 

Sect. IV. Friction of the engines, detemuned by 

the dynamometer .213 

Sect. V. Friction of the engines, determined by the 

angle of friction .... 214 

Sect. VI. Table of the results of the preceding ex- 
periments on the friction of unloaded 
locomotive engines .217 

Sect. VII. Of the friction of the mechanical organs 
of the engine, and of its friction as a 
carriage 220 



I 

Xlii CONTENTS. 



PA6S 



Article II. Of the addUional friction of loaded loco- 
motive engines. 

Sect. I. Of the mode of determination . 223 

Sect. II. Ekperiments on the additional friction of 

loaded locomotive engines . 228 

Sect. III. New devdopements on the mode of deter- 
mination employed . . . 235 



CHAPTER IX. 

OF THE TOTAL RB8IBTANCE ON THE PISTON, RESULTING 
PROM THE DIVERS PARTIAL RESISTANCES PRECEDENTLT 
MEASURED ........ 238 



CHAPTER X. 

OF THE VAPORIZATION OF LOCOMOTIVE ENGINES. 

Sect. I. Experiments on the vaporization of loco- 
motive engines .... 247 

Sect. II. Of the influence of the pressure in the 
boiler on the vaporization of the 
engine 254 

Sect. III. Of the influence of the velocity of the 
engine on the vaporization of the 
boiler 259 

Sect. IV. Of the influence of the orifice of the blast- 
pipe on the vaporization of locomotive 
engines ..... 263 

Sect. V. Of the comparative vaporization of the 
fire-box and the tubes, > and of the 
definitive vaporization of the engines 
per unit of heating surface of their 
boiler 266 



CONTEXTS. xliii 

PAGE 

Sect. VI. Of the loss of steam which takes place 
by the safety* valves, during the work 
of locomotive engines . . 274 

Sect. VII. Of the water drawn into the cyhnders 
in its liquid state, and of the effective 
vaporization of the engines . 282 



CHAPTER XI. 

OF FUBL. 

Sect. I. Experiments on the consumption of fuel 
necessary ta produce, in locomotive 
engines, a given vaporization . 296 

Sect. II. Of the most advantageous proportion .to 
establish between the fire-box and the 
tubes of the boiler, in locomotive 
engines ..... 301 

Sect. III. Of the consumption of fuel necessary to 

draw a given load a given distance 307 



CHAPTER XII. 

THBORT OF LOCOMOTIVB BNOINBS. 

Articlb I. Of the effects of the engines with an indefinite 

. load or velocity. 

Sect. I. Of the different problems which present 
themselves in the calculation of the 
effects of locomotive engines .317 

Sect. II. Of the elements to be considered in the 

calculation of the engines . .319 

Sect. III. Of the pressure of the steam in the 

cylinder 325 



Xliy CONTENTS. 

PAOB 

Sect. IV. Of the velocity of the eng^e with a given 

load 330 

Sect. V. Of the load of the engine for a desired 

velocity 344 

Sect. VI. Of the different expressions of the useful 

effect of the engine . . 350 

Article II. Of the nuunmum useful effect of the engine. 

Sect. I. Of the velocity of maximum useful effect 362 
Sect. II. Of the load corresponding to the maxi- 
mum of useful effect . 365 
Sect. III. Of the measure of the maximum usefdl 

effect of the engine 367 

Articlb III. Practictd formula for calculating the effects 

of locomotive engines, and examples of 
their (plication .... 368 

Article IV. Experiments on the velocity and load of the 

engines ...... 382 



CHAPTER XIII. 

OF THS PROPORTIONS OF LOCOMOTIVE ENGINES. 

Sect. I. Of the divers problems which occur in 

the construction of locomotive engines 395 

Sect. II. Of the vaporization, or of the heating 
surfeure, necessary to enable a locomo- 
tive engine to draw a given load at a 
desired velocity . . . •. 397 

Sect. III. Of the diameter of the cylinders, neces- 
sary that the engine may draw a given 
load at a given velocity 400 



CONTEXTS. Xlv 

PAOB 

Sect. IV. Of the length of the stroke of the piston, 
requisite for the engine to draw a 
given load at a g^ven velocity . . 402 

Sect. V. Of the diameter of the wheel, necessary 
for the engine to attain a desired 
velocity with a given load 403 

Sect. VI. Of the vaporization, or of the heating 

.sur&ce a locomotive engine onght to 

have, in order to acquire a given 

velocity, producing at the same time 

its maximum of useful effect . 404 

Sect. VII. Of the pressure in the hoiler necessary 
for the engine to draw a given load, 
or acquire a desired velocity, pro- 
ducing at the same time its maximum 
of useful effect .... 406 

Sect. VIII. Of the diameter of the cylinder, or of the 
stroke of the piston, or of the diame- 
ter of the wheel, necessary that an 
engine may assume a desired velocity, 
or draw a given load, producing also 
its maximum useful effect 408 

Sect. IX. Of the combined proportions to be given 
to the parts of an engine, to enable it 
to fulfil divers simultaneous conditions 411 

Sect. X. Of the special influence of each of the 
dimensions of the engine on the eflects 
produced 417 

Sect. XI. Of the comparative effects of locomotive 
engines upon the wide-g^uge and nar- 
row-gauge railways 423 

Sect. XII. Practical formulae, to determine the pro- 
portions of locomotive engines, accord- 
ing to given conditions . .431 



Xlvi CONTENTS. 



PAGE 



CHAPTER XIV. 

OF ADHESION 434 



CHAPTER XV. 

OF THE RSOULATOR. 



Sect. I. Of the effects of the regulator on the 

velocity of the engine . . 439 

Sect. II. Dimensions of the steam-passages in some 

locomotive engines . . 445 



CHAPTER XVI. 

OF THB LEAD OF THE SLIDE. 

Sect. I. Of the nature and effects of the lead of the 

slide 447 

Sect. II. Of the effects of the lead of the slide on 

the velocity of the engine . . 455 

Sect. III. Of the effects of the lead of the slide on 
the maximum load of which the engine 
is capable 460 

Sect. IV. Of the manner of regulating the lead 

of the slide 466 



CHAPTER XVII. 

OF INCLINED PLANES. 

Sect. I. Of the load on a level » which corresponds 
to the load on a given inclined plane, 
and vice versd .470 



CONTENTS. Xlvii 

PAGE 

Sect. II. Of the velocity of locomotive engines on 

inclined planes . . .476 

Sect. III. Of the velocity of descent of trains, 
on inclined planes where no use is 
made of the force of the engine . 480 

Sect. IV. Of the duration of the trip, and of the 
average velocity of the engines, on a 
svstem of successive inclinations . 486 

Sect. V. Of the average load of the engines, 
during their passage over a system 
of successive planes • . . 490 

Sect. vj. Of the quantity of work on a level, which 
corresponds to the conveyance of a 
given load, over a system of known 
inclinations ..... 495 

Sect. VII. Of the means of ascending inclined 

planes on railways . . . .510 

Sect. vni. Of the best line for a railway between 

two given points .... 514 



CHAPTER XVIII. 



OF CUBVBS. 



Sect. I. Of the effects of curves on railways . 521 

Sect. II. Of curves the resistance of which is 
corrected bv the conical inclination 
of the wheels of the waggons . 522 

Sect. III. Of the superelevation of the outer rail to 
be employed in curves whose curvature . 
is not corrected by the conical inclina- 
tion of the wheels . . . .532 



Xlviii CONTENTS. 



PAGE 



APPENDIX. 

EXPENSES OF HAULAGE BT LOCOMOTIVE ENGINES ON 

RAILWAYS .... 537 

Sect. I. Expense for repairs of locomotive engines 538 
Sect. II. Expense of fuel '. .551 

Sect. III. Expense of locomotive power . 553 

Sect. IV. Expense for maintenance of way . 555 

Sect. V. Total expense of haulage 559 

Sect. VI. Of the expense of horses employed as 

a moving power . .569 

Sect. VII. Of the net profits . .571 

Receipts and expenditure of the Liverpool 
and Manchester Railway, from the 
commencement of the undertaking to 
30th June, 1834 .573 



Page 307.— Read Skct. III. 



A PRACTICAL TREATISE 



ON 



LOCOMOTIVE ENGINES; 



CHAPTER I. 
DESCRIPTION OF A LOCOMOTIVE ENGINE. 



hf 



ARTICLE I. 

DETAIL AND DISPOSITION OF THE PARTS. 

Sect. L Of the Boiler. 

The plan adopted in this work will, it is hoped, 
render it both clear and methodical. 

We shall begin by a succinct description of a 
locomotive engine, in order first of all to set before 
the eyes of the reader the machine which is the 
subject of consideration. 

We shall then explain the laws which regulate 
the mechanical action of the steam, and describe 
the instruments in use to measure its pressure ; 
which will make known the agent employed to 
produce the motion of the engine. 

Our attention will afterwards be directed towards 
the resistances which the engine in its motion has 

B 



I CHAPTER I. 

to overcome, so that we shall successively en- 
deavour to determine as well the resistance jof the 
waggons as that which belongs to the engine itself, 
either when it moves alone or when it draws a 
load after it. 

With these primary data we shall pass to the 
general theory of the motion of locomotive engines, 
and shall lay down the formulae by which to de- 
termine, a priori, either the speed the engine will 
assume with a given load, the load it will draw at 
a given speed, or the proportions which are to be 
adopted in its construction, in order to obtain any 
intended effect. 

We shall then have to consider several addi- 
tional dispositions proper to the engine, which may 
exercise more or less influence on the expected 
effects ; and we shall also treat of some external 
circumstances, the result of which may be of the 
same nature. 

Lastly, we shall show the engine's consumption 
of fuel with given loads, and every other kind of 
expenditure to which it gives rise. 

These inquiries give the solution of all the most 
important questions concerning the application of 
locomotive engines to the draught of loads. They 
will sometimes be necessarily subdivided into several 
branches, and require calculations and theoretical 
illustrations, of more Or less extent, though always 
plain and easy, and a series of experiments more 
or less numerous ; but we shall take care to main- 



DESCRIPTION. 3 

tain, all through our work, the classification we at 
present lay down. We begin then by the descrip- 
tion of the engine. 

Plate I. represents a six-wheel locomotive engine, 
followed by its tender. Plates II. and III. represent 
a locomotive with four wheels. The mechanism 
of these engines is sufficiently simple for a short 
description to make their mode of acting under- 
stood; which is the only object here intended. 
Moreover, whatever this first cursory view may 
leave imperfect will be found illustrated by the 
developements which we shall have occasion to give 
in the course of the work. 

The principal parts of the engine are : the fire- 
place and boiler, which constitute the means of 
raising the steam ; the slides and cylinders, which 
are the means of bringing into action the elastic 
force residing in that steam; and the cranks and 
wheels, by means of which the motion is transferred 
from the piston to the engine itself. After having 
described those principal parts, we shall pass to some 
others of less importance, and then show the particu- 
lar place each of those parts occupy in the engine. 

Figure 5 gives a complete idea of the boiler. 

It shows the body of the machine, composed of 
three distinct compartments. That on the right, 
or in front of the engine, and which is surmounted 
by the chimney C, is called the smoke-box. It is 
separated from the two others by a partition tt. 
The two other compartments together form the 



4 CHAPTER I. 

boiler: the hinder one is called the fire-box, and 
the middle one, or cylindrical part, is the boiler 
properly so called. Both the latter compartments 
are filled with water to a certain height cd, but 
part of their internal space is occupied by the fire, 
as will be explained. 

In the hindmost compartment is placed a square 
box c, which contains the fuel, or forms the fire- 
place of the engine. Between the sides of that 
box and those of the compartment in which it is 
contained, a space qq is left, which communicates 
freely with the remainder of the boiler, and which 
is consequently filled with water. The fire-place 
is supported in the corresponding compartment, 
and joined to it by strong bolts, having the ad- 
vantage of giving soUdity to that part of the boiler 
which, not being rounded, ofiers less resistance than 
the cyUndrical parts. 

The fire-place e, being thus placed in the middle 
of one of the compartments of the boiler, would 
be surrounded on all sides with water, were it not 
for the aperture Z, which forms the door of the fire- 
place, and the bottom, nriy of the box, which is occu- 
pied by a grate, one of the bars of which is repre- 
sented at nn. This grate is more plainly shown 
in fig. 6, which represents the same fire-box seen in 
front. 

Near the door I, and on the engine, is placed 
a strong supporting plate of iron, represented in 
figs. 1 and 2, by BB. The use of this plate is for 



DESCRIPTION. 5 

the engine-man to stand upon. Directly behind 
the engine comes the tender-carriage for coke and 
water, so that it is easy for the fireman to throw 
coke on the fire by the door I, and to let water pass 
into the boiler, whenever it may be necessary. This 
supply of water takes place by means of a forcing- 
pump, put in motion by the engine itself, and which 
will be spoken of hereafter. 

The lower part, ntij of the fire-place is occupied, 
as we have said, by a grate, and remains conse- 
quently open, admitting the external air required 
for the combustion of the fuel. The coke thrown 
into the fire-place faUs on the grate and is sup- 
ported by it. When the fire is lighted, and the 
door is shut, the flame of the fuel remains con- 
fined in the fire-place. It would have no egress 
if a number of small tubes or flues e'e'^ the dispo- 
sition of which is better seen in fig. 6, were not to 
lead the flame to the chimney, after passing through 
the whole length of the second compartment or 
cylindrical part of the boiler. 

From this construction it will easily be conceived, 
that as the fire is shut up in the fire-box, and 
completely surrounded with water, none of its calo- 
rific parts are lost. Afterwards, the flame, in its 
way to the chimney, divides itself among all the 
small flues above mentioned. It thus traverses the 
water of the boiler, having a considerable surface 
in contact with it, and only escapes after having 
communicated to the water as much as possible of 



6 CHAPTER I. 

the caloric it contained. Once arrived at the ex- 
tremity f!' of the tubes^ the flame spreads itself in 
the smoke-box, and escapes freely through the 
chimney C. 

We see thus the heat applied here in two dis- 
tinct manners. All the water which surrounds the 
fire-place is in contact with the ignited fuel; and 
the water which is placed in the middle compart- 
ment is in contact with the inflamed gases which 
issue from the fire-place. We shall refer again to 
this distinction, in treating of the vaporization of 
the boilers, and we shall endeavour to ascertain if 
the efiects produced in each compartment difier 
from each other. 

To this form of boiler is to be attributed all the 
astonishing power of locomotives at the present day. 
It pennits, in fact, exposing a very large extent of 
surface to the action of the fire, and consequently 
to develope a considerable quantity of steam, using 
at the same time a boiler of very small dimensions, 
which is necessary for engines which have to carry 
their own weight wdth their load. And, moreover, 
it must be remarked that all the efiect produced 
by the tubes is obtained without burning any more 
coal, and in merely employing the caloric, which 
would otherwise be lost. As in the action of loco- 
motives, all finally depends on the quantity of steam 
that can be developed in the boiler in a given time 
with the least possible expense, it will readily be 
conceived that this invention is unquestionably the 



DBSCRIPTION. 



most important that has been introduced into the 
construction of locomotives since their. origin. 

It may be necessary to observe here, that this 
form of a boiler, with tubes, is a French invention. 
This ingenious idea belongs to M. Seguin, civil 
engineer and manufacturer in Annonay.^ 



^ M. Segain'8 patent bears the date of the 22nd of February, 
1828 ; and it was not until April 25, 1829, that the committee of 
directors of the liyerpool Railway called the attention of the 
English mechanicians towards locomotive engines, by proposing 
a prize on the subject. On October 6, of the same year, 1829, 
and not before, appeared the Rocket engine of Messrs. Stephenson 
and Booth, the principle and even the form of which difier in no 
way from M. Segpiin's patent. Without then by any means 
detracting from Mr. Booth's merit in having also conceived that 
ingenious idea, the prior claim rests, nevertheless, with the 
French engineer. 

The fact may be easily verified in England, by looking for a 
description of the patent in some of the following works, which 
are certainly to be found in the British Museum and other chief 
Elnglish libraries : Anmales de l' Industrie JFhm^aise et Etranghv, 
ou Recueil Industriel et Manufacturier, atmie 1828 ; Bulletin de la 
Sociiti d' Encouragement pour V Industrie Nationale, amnie 1828 ; 
Descr^tion des Machines et Procid^s cansignds dans les Brevets 
d'Invention, de Perfectionnement et d* Importation^ publi^e d'aprks 
les Ordres du MuUstre de I'IntMeur et du Commerce. This last 
work only gives the description of expired patents ; so that M. 
Seguin's will be found in the year 1838. 

In an American edition of Wood's work on Railways (page 
338) we find, that in 1825 Mr. John Stevens, of Hoboken in the 
State of New Jersey, constructed and employed a locomotive 
engine, the boiler of which consisted entirely of tubes of very 
small diameter filled with water. But as in the boilers we speak 



8 CHAPTER I. 

Sect. II. Of the Action of the Cylinders. 

The second important part of the engine is the 
apparatus of slides and cylinders. Fig. 5 is also 
designed to show its disposition. 

In the upper part of the boiler, that is to say, in 
the part occupied by the steam, is a large tube 
VW", called the steam-pipe. It is open at one 
end V, and leads out of the boiler. By this tube 
the steam is conducted into the cylinders. At V, 
in the interior of the tube, is a cock or regulator, 
the handle T of which extends out of the engine. 
By turning that handle more or less, the passage for 
the steam may be opened or shut at will. 

The steam, being generated in great abundance in 
the boiler, and unable to escape out of it, acquires a 
considerable degree of elastic force. If at that mo- 
ment the cock V^ is opened, the steam, penetrating 
into the tube by the aperture V, follows it to the 
entrance v of the slide-box. There a sliding valve 
X, which moves at the same time with the engine, 
opens a communication to the steam successively 
with each end of the cylinders, and this steam 
drives the piston alternately from one extremity of 
the cylinders to the other. The cylinders are 



of, it is the flame and not the water that fills the tubes, which 
totally changes the principle of their construction, the ftict re- 
ported by the American editor does not disprove the remark 
established above. 



DESCRIPTION. y 

placed horizontally at the bottom of the smoke-box, 
where the passage of the flame and the sides of that 
box protect them against the condensing effect of 
the cold air, and keep them in a proper degree 
of heat. 

The direction of the arrows in the figure marks 
the line of circulation followed by the steam, from 
its entrance at the aperture V, as far as the slide- 
box. In the situation in which the slide is here 
represented, passage 1 is open to the steam, and 
consequently the piston is pushed in the direction 
of the arrow. At the following instant, passage 2 
will be open in its turn, and the piston will be 
pushed the contrary way. When the steam has 
produced its effect, it passes into the tube v\ and is 
conveyed by it to the chimney, through which it 
escapes into the atmosphere. 

The introduction of the steam takes place at V, 
in a dome called the steam-dome, purposely ele- 
vated, that the jolting of the engine and the ebul- 
lition may not cause the water of the boiler to get 
into the opening V. 



Sbct. hi. Of the Cranks and Wheels. 

The piston-rods being set in motion according to 
the foregoing explanation, and sliding in guides 
which prevent any deviation from a rectilinear 
horizontal motion, communicate a rotatory move- 
ment to the axle of the two large or drawing 



10 CHAPTER I. 

wheels of the engine. The transformation of the 
alternate motion into a circular one, takes place 
after the manner of the conmion foot spinning- 
wheel, by means of a crank in the axle. This 
effect is clearly represented in fig. 5. There the 
steam may be seen forcing alternately the piston 
backwards and forwards, and turning the crank yz^ 
and at the same time the axle and the wheel which 
is fixed to it. However, as in the motion of a 
crank, there are two points in which the alternate 
force that puts it in motion has no greater ten- 
dency to move it in one direction than in another, 
which takes place when the radius of the crank 
happens to be in the direction of the alternate 
motion, the two cranks, respectively corresponding 
with the two pistons, are placed at right angles to 
each other. By that means one of the two has 
always its full effect whenever the other ceases to 
act, and the power of the engine does not vary. 
Tlie two cylinders being placed, as we have already 
said, in the lower part of the smoke-box, the piston- 
rods communicate directly under the engine with 
the two cranks, as appears in the figure. The 
crank-axle being set in motion, the wheels, which 
form one body with it, turn at the same time, and 
the engine is propelled in the same manner as a 
carriage which is set agoing by turning the wheels 
round by the spokes. 

The only fulcrum of the motion being in the 
adhesion of the wheels to the rails that support 



DESCRIPTION. 11 

them, which adhesion causes them to advance in- 
stead of slipping round, it might appear doubtfiil 
whether, on such an even surface as the rails of a 
railroad, the engine could advance by means of the 
sole rotatory motion imparted to its wheels, par- 
ticularly^hen the engine has to draw a considerable 
weight. But experience proves, that however slight 
the adhesion of a wheel to a well-polished rail may 
appear to be, as, on the other hand, the power 
required to draw a load on a railroad is very small, 
that adhesion is sufficient, and the engine pro* 
gresses, followed by its whole train. 

In ordinary cases the adhesion of two wheels is 
sufficient; particularly with engines the weight of 
which is so distributed that the drawing-wheels bear 
a large portion of it. When a great power of ad- 
hesion is required all the wheels are made equal. 
In that case, if necessary, the wheels of the same 
side may be connected together by metallic rods 
placed on the outside of the wheels. One of these 
connecting-rods is represented in fig. 35, Plate IIL 
C is the prolongation of the axle beyond the wheel. 
The crank-arm Co is festened to that prolongation 
of the axle, and must necessarily turn with it. The 
point is a ball and socket joint ; m is a cotton- 
wick Sjrphon, by which the oil is fed into the joint ; 
nn are keys designed to lengthen or shorten the rod, 
which at its opposite end is joined in the same 
manner to the crank-arm of the other wheel. The 
natural result of this is, that when the wheel or the 



' 



12 CHAPTER I. 

axle C turns, it carries along with it the crank-arm 
Co, and thus communicates the same motion to the 
other extremity of the connecting-rod, and by it to 
the crank-arm of the second axle. Thus the motion 
of the machinery is communicated by the two 
working wheels to the others, and the engine then 
adheres by all its wheels. 

In order that, while in motion, the engine may 
not sUp off the rails, which, we know, are iron bars 
projecting above the ground, the wheels have, on 
the inner side, a flange that prevents any lateral 
motion. But as, on the other hand, that flange 
ought not to be in danger of constantly rubbing 
against the side of the rail, the tire of the wheel 
is not exactly cylindrical, but slightly conical. Its 
diameter is a little larger on the side of the flange 
than on the outward side; the consequence of 
which is, that, supposing the engine were to be for 
a moment pushed to the left, the left wheel, resting 
on its broadest part, would pass over more way than 
the right wheel, and by that means bring the engine 
back to its true place between the rails. Wheels of 
such a form may be seen in figs. 3 and 4. 



Sect. IV. Of the Safety Valves. 

The three preceding points form the foundation 
of the play of the engine; the other parts are 
merely accessory, that is to say, essential only to 
the setting of the former in action. The boiler has 



DESCRIPTION. 13 

two safety-valves E, F (figs. 1 and 2), one of which, 
F, is sometimes shut up in a box^ to put it out of 
the reach of the engine-man, and to prevent him 
from overcharging it, as he might be tempted to do 
in order to obtain from the engine a greater effect, 
even at the risk of damaging it. More commonly, 
however, this precaution is given up, on account of 
its inconvenience. 

The object of these valves is to let the steam 
escape into the atmosphere, as soon as its elastic 
force attains a limit beyond which it might be dan- 
gerous to the boiler. They may also, by being 
properly loosened, be used to measure the pressure 
of the steam ; but as this point demands some de- 
velopement, we shall hereafter make it the subject 
of a chapter. 

Sect. V. Of the Water-Gauge. 

A gauge is likewise fixed to the engine to show 
at what height the water stands in the boiler. This 
gauge is a glass tube, mn (fig. 7), enchased at both 
its ends in two verrels aa, with cocks communi- 
cating with the interior of the boiler and appearing 
outside, as may be seen in the figure. When the 
two cocks rr at top and bottom of the tube are 
opened, the water penetrates into the tube and takes 
the same level as in the boiler. The cock S is 
designed to let that water afterwards run off. This 
instrument informs the engine-man when the ap- 



14 CHAPTER I. 

paratus wants a supply from the pump. As, how- 
ever, the tubes and other parts of the boiler begin 
to suffer, that is to say, are apt to crack, when the 
water gets too low in the engine, there are, for still 
further surety, on the side of the boiler, two and 
sometimes three small cocks, placed at different 
heights ; by opening which, one after the other, the 
level of the water in the interior may be also as- 
certained. 

Sect. VI. 0/ the Slides. 

Another important object yet remains to be elu- 
cidated. We have said above that the slide-valve 
admits successively the steam above and below the 
piston of each cylinder, the result of which is the 
alternate motion, source of the final progressive 
motion of the engine. The engine-man then having 
opened the regulator or cock that admits the steam 
into the pipes, the steam proceeds from the boiler 
through the tube v (fig. 8) into the steam-chest or 
sUde-box, and, pressing with all its force on the 
upper part x of the sliding-valve, compels it to 
remain in immediate contact with the plane on 
which it slides while performing its motion. When 
the slide is in the situation in which it is repre- 
sented in fig. 8, the steam takes the way marked 1 , 
acts upon the piston, and pushes it in the direction 
of the arrow. In the meanwhile, the steam under 
the piston escapes through the passage 2, which 
then communicates with the atmosphere by means 



DESCRIPTION. 15 

of the aperture e. When this first effect has been 
produced y the slide, by means of its rod /, is pushed 
in the position marked by the dotted lines. Then, 
on the contrary, it is the passage 2 which is open to 
the steam !Zing from the iSer: it pushes con- 
sequently, the piston in the opposite direction to its 
first motion, while the passage 1, communicating 
in its turn with the aperture e, gives free egress to 
the steam that has produced its effect. The al- 
ternate motion continues thus: the slide passing 
from one position to the other, by which it opens 
and shuts successively the passages or steam-ports, 
so that the steam may act alternately above and 
below the piston. The steam is afterwards led to 
the chimney, as will be explained hereafter, there to 
augment the current of air by which is caused the 
draught of the fire. 

The motion of the slide is regulated in such wise 
that, in accompanying the motion of the piston, it 
nevertheless precedes it by an instant of time ; that 
is to say, instead of opening the passage for the 
stroke of the piston, just at the moment the piston 
is about to begin that stroke, it opens it a httle 
beforehand. We shall have occasion to come back 
to this point, and it will appear that this disposition, 
favourable to the speed of the engine, may be ad- 
vantageously employed within certain limits; but 
that beyond those limits it is prejudicial to the 
maximum load which the engine is able to draw. 



16 CHAPTER I. 

Sect. VII. Of the Eccentric Motion. 

The alternate motion of the slide is performed by 
the steam itself. Some attention is requisite to get 
a clear conception of this. 

An eccentric wheel is fastened to the axle, and 
while the axle turns, the eccentric, drawn along by 
its motion, pushes and draws alternately the rod of 
the slide. 

This effect is represented in figures 9 and 10. 
The point O is the centre of the axle, the section of 
wliich is here hatched. The point m is the centre 
of the eccentric, hatched in a contrary direction. 
The axle, in turning, draws the eccentric along with 
it, and consequently makes the point m describe a 
circle round the point O. In that motion the point 
m, passing successively to the right and the left of 
the centre O, must necessarily push and draw 
alternately the shaft L, which acts upon the slides. 

On the other hand, the point C representing the 
extremity or throw of the crank of the axle, which 
is set in motion by the piston, it will appear that 
when the steam, pushing the piston from oue end of 
the cylinder to the other, makes the crank revolve 
half-way round, the axle makes also the half of a 
revolution round itself; therefore the point m de- 
scribes the half of a circumference round the point 
O, and consequently the eccentric pushes the slide- 
rod /, from one of its extreme positions to the other, 
that is, from one end of its stroke to the other. 



DESCRIPTION. 17 

Thus placed, by this first operation, the slide now 
admits the steam on the opposite side of the piston. 
The piston then goes back, makes the axle revolve 
again half-way round, whereby the slide is brought 
back to its original position, which suits the next 
stroke of the piston ; and so on. 

The effect of drawing and pushing alternately the 
slide-rod, by means of the rotation of the eccentric, 
is accomplished by a metallic ring nn fixed to the 
end of the shaft L, and in which the eccentric 
wheel turns, the surfaces which are in contact being 
smooth and lubricated with oil. By this arrange- 
ment, while the great radius of the eccentric passes, 
in turning, from one side of the centre to the other, 
it carries along with it the shaft fastened to the 
ring, and communicates to that shaft the alternate 
motion. 

By this it will be seen that the eccentric wheel 
acts here the part of a common crank, for trans- 
forming the circular motion of the axle into an 
alternate motion applied to the slide, on the con- 
trary principle to that which changes the alternate 
motion of the piston into a circular motion applied 
to the axle of the engine ; but the eccentric dis* 
penses with the crank which would have been 
necessary in the axle. 

However, as by the disposition of the engine the 
slide-rod is not in the same plane with the axle, the 
eccentric does not communicate the motion directly 
to the slide-rod itself, but by means of the cross** 

c 



18 CHAPTER I. 

axle VKl\ whose fixed point is at K; and the 
consequence is, that when the eccentric goes back, 
the slide-rod advances, and mce versdy as may be 
seen in the figure. 

A comparison between the figs. 9 and 10, the 
difierence of which is a quarter of a revolution, will 
make the above-mentioned effects perfectly intel- 
ligible. 

By examining the motion of the slide (figs. 10 
and 26) it will be seen, that while passing from one 
of its situations to the other, and when it happens 
to be in the middle position, there occurs an instant 
during which both the passages or steam-ports are 
shut. This efiect takes place at the moment the 
slide changes the passages of the steam, and cor- 
responds with the point where the piston changes 
its direction. This coincidence can only take place 
because, setting aside the lead of the slide, the 
radius of the eccentric is at right angles with the 
radius of the crank. In fact, the slide is necessarily 
thus in its middle position, that is to say, changing 
the conmnmications of the steam, at the same time 
as the piston is at the bottom of the cylinder, ready 
also to alter the direction of its motion. This cor- 
relativeness of motions is clearly exhibited in the 
figure. 

The particular advantage of the eccentric being 
thus placed at right angles with the crank is, that 
the eccentric is in full action when the crank is on 
its centre, or the piston at the bottom of the cy- 



DESCRIPTION. 19 

linder : that is to say, that the slide is in its most 
rapid motion just at the moment that it is to open 
or shut the steam-ports; which circumstance is 
necessary, to prevent time being lost in the al- 
ternate effect of the steam. 

In order that the steam-ports may not begin to 
close immediately after having been opened, the 
slide is so disposed, that after having uncovered one 
of the ports, it continues its motion for a short space 
before beginning to return. This effect, which is 
called the travel of the slide, is represented in the 
figs. 9 and 11. By this disposition the uncovered 
port remains entirely open while the slide is per- 
forming its travel going and coming, and the op- 
posite port continues to be entirely closed. It will 
be remarked that this part of the motion of the 
slide is precisely the slowest of its stroke ; but as 
the slide begins to pass again over the steam-ports, 
it acquires, on the contrary, its greatest velocity, 
because the eccentric is then in its most rapid 
motion. This disposition then causes the apertures 
to be entirely open or closed during the greater part 
of the time employed in performmg each stroke, 
and to change them as suddenly as possible at the 
most favourable moment for so doing. 

That the travel of the sUde may not have the 
effect of reducing too much the eduction-port e, 
care is taken to make the latter of such width that, 
notwithstanding the portion of it which is covered 
by the flange of the sUde, it still retains a width 



20 CHAPTER I. 

equal to that of each of the other steam-ports. 
Thus, for instance, the width of the steam-ports 
is 1 inch each; that of the bars, or separations 
between the ports, 1 inch ; and the eduction-port e, 
Ijt inch. Then, exclusive of the slight overlap of 
the slide, of which we shall presently speak, the 
slide may have a travel of ^ inch ; for it is plain 
that in the extreme position of the latter, the educ- 
tion-port will never be reduced to less than an inch, 
which is the width of the steam-ports. 

Finally, when the slide is in its mean position, 
it not only intercepts at once both the steam-ports, 
as is seen represented in figs. 10 and 26, but it 
overlaps them by a small flange, the object of which 
is to remove all possibility of one of the passages 
ever being open before the other is completely 
closed. This overlap is usually from ^ to i inch, 
and it is plain that, being added to each side of 
the slide, it diminishes by so much the travel of 
the latter, as has been said above. 



Sect. VIII. Of the Drivers. 

Until now we have spoken as if there were only 
one sUde, but, having said there are two cylinders, 
it is clear that there must be a sUde, and conse- 
quently an eccentric, to each of them. On the 
other hand, the two pistons, alternating one with 
the lOther in their motion, that is to say, acting 



r 



DESCRIPTION. 21 

upon two cranks perpendicular to each other, as 
has been explained, the radii of the two eccentrics 
must necessarily stand also at right angles with 
each other. This disposition may be seen in figs. 1 1 
and 12, where the piece forming the two eccentrics 
is represented in front. To make it more clear it 
is marked by hatchings. 

This piece must, as has been said, move with 
and be carried along by the axle. However, if it 
were permanently fixed on the axle, its position 
might suit when the engine is going forward, and 
not when it is to go backward ; for it will be seen 
that, for these two motions, the eccentric must 
be fixed in two difierent positions. 

This piece is therefore loose upon the axle, like a 
pulley on its axis, but it can be fastened to it at 
will. To that efiect it has two apertures, repre- 
sented at O and O"; and the axle itself carries 
two pins tt\ which are called drivers. The 
eccentric being placed on the axle between the 
two drivers, it is easy to push it, by means of 
a lever, either against one or against the other, 
until the driver enters into the aperture designed 
for it; so that from that moment the eccentric 
may be drawn along by the axle. Moreover, if these 
two drivers be placed in such a manner that one 
may suit the progressive, and the other the retro- 
grade, motion of the engine, then, by shifting the 
eccentric fix)m the one to the other, the engine may 



i 



22 CHAPTER I. 

be made to go either forward or backward at plea- 
sure. 

There is no difficulty in fixing the place that the 
eccentric must occupy on the axle, either for the 
progressive or for the retrograde motion. 

Let us suppose, that by pushing the engine 
gently along the rails, we bring one of the pis- 
tons to be just in the middle of the cylinder, and 
that precisely at the same instant, the crank on 
which that piston acts is in its vertical position 
above the axle, as in fig. 5 ; it is dear that, to make 
the engine go forward, the steam must push the 
piston forwards, for then the piston will carry along 
with it, in the same direction, both the crank and 
the wheels. Consequently the slide must admit the 
steam by the port No. 1, or be drawn forward as it 
is represented in fig. 5, which, by referring to fig. 9, 
requires that the radius of the eccentric be hori- 
zontal, and placed at the back of the axle. This 
is therefore the point at which the driver must fix 
the eccentric for the progressive motion. 

The engine remaining in the same position, 
let us suppose, that we wish, on the contrary, to 
dispose it for the retrograde motion. The steam 
must arrive on the opposite face of the piston, that 
is, the port No. 2 must be opened to it; which 
supposes that the slide is pushed backwards, and 
consequently that the eccentric is in fix)nt. It is 
therefore horizontally, and in front of the axle, 



DESCRIPTION. 23 

that the eccentric must be fixed by means of the 
driver. 

This is exactly the position of fig. 12. By ob- 
serving the crank A, we see that while that crank 
is vertical and above the axle, the driver r, and 
the aperture that receives it, are behind, and hidden 
by the axle; consequently, the eccentric is hori- 
zontal, and in front, — a position which, as we have 
seen, suits the retrograde motion. The driver r is 
therefore placed for the retrograde motion, since 
it keeps the eccentric in that position. 

To return to the first case, if we now suppose, 
on the contrary, that the eccentric be pushed against 
the other driver r , the corresponding aperture of the 
eccentric being at (X, that is to say, not being in 
firont of the driver, the consequence will be that, 
the eccentric not stirring out of its place, the axle 
will have to turn half round before the driver can 
enter into the aperture. From this it follows, that 
if we continue to examine the crank A, it will be 
found to have arrived under the axle, while the 
eccentric will still be in the front, which is the 
poution that suits the progressive motion ; for it is 
the same as that of the crank above the axle and 
the eccentric behind, which has been explained 
above. 

Thus, we see that the two drivers / and r, in 
figs. 1 1 and 12, being placed at right angles with 
each other, and with the cranks of the axle, are 
in a proper position, one for the progressive, and 



24 CHAPTER I. 

the other for the retrograde, motion of the engine ; 
and that by pushing the eccentric, by means of a 
lever, either on the one or on the other of the 
drivers, the effect of the steam on the piston will 
immediately be to carry the engine either forwards 
or backwards, according to the driver with which 
it has been thrown in gear. The lever which causes 
the change of position of the eccentric, is placed 
in such a manner as to present its handle within the 
reach of the engine-man^ on the plate on which 
he stands. 

Besides these several dispositions, in order that 
the man who directs the engine may, himself and of 
his own accord, move the sUdes independently of 
the motion of the axle, the shafts of the eccentrics 
are not invariably fixed to the slide-rods. They are 
only fastened to them by a notch U, figs. 13 and 
14. By means of a lever acting on the small rod 
vfiloy the engine-man can raise the shaft of the 
eccentric and disengage it from the notch, as may 
be seen in fig. 14. Then the slides are at Uberty to 
move independently of the axle ; and therefore it is 
easy, by means of two handles represented by PP, 
in figs. 2, 3, 4, and connected with the sUde-rods, 
to give to the slides the required motion. 

In some modem engines, four eccentrics are 
employed instead of two ; namely, two for the pro- 
gressive motion of the engine, and two for the re- 
trograde; either pair being set according to the 
direction in which the engine is intended to move. 



DESCRIPTION. 25 

This arrangement advantageously supplies the place 
of the drivers, because it is of a surer effect; but as, 
with respect to explication, it amounts precisely to 
the same, we shall not here enter into the detail of 
that construction. 



Sect. IX. Of the Pumps. 

Under the body of the engine are two pumps p^ 
(fig. 2,) the use of which is to replenish the boiler 
with water. Each of them is placed immediately 
under the piston-rod of each cylinder, and is worked 
by it. Each pump sucks the water of the tender 
into the cylinder of the pump, on the one hand, and 
on the other hand, forces it from the cylinder of the 
pump into the boiler, in the usual way. By having 
two pumps the replenishing of the boiler is secured, 
as, in case one of the two were to get out of order, 
the other may easily supply its place. These pumps 
are in continual action; yet they can only force 
water into the boiler when the cock of the suction- 
pipe is opened, thereby to let the water of the 
tender come into the cylinder of the pump. 

The valve of these pumps is ingeniously made of 
a small metallic sphere, resting on a circular seat, 
on which it always exactly fits. Its action takes 
place by rising within a cylinder, the sides of which 
are pierced with four apertures for the passage of 
the water. One of these valves is represented in 
fig. 15. The water is introduced through er, from 



26 CHAPTER I. 

the interior of the cylmder> under the spherical ball 
which it raises, and is diflPdsed in the body of the 
pump by the apertures b b. This form of a valve 
never misses its effect; and the pumps which, in 
the beginning, were continually out of order, are 
free from that defect, since Mr. John Melling, of 
Liverpool, first introduced that sort of valve. 

Sect. X. Of the Regulator. 

The regulator, of which we have spoken above, 
and by means of which the passage leading from 
the boiler to the cylinders may be more or less 
opened, is represented in figs. 32 and 33. It simply 
consists of two metallic disks placed above and 
exactly fitting each other, both having an aperture 
of the same size. The inferior disk is immoveable, 
and shuts the pipe through which the steam es- 
capes. The superior disk is moveable, by means of 
a handle T, which projects out of the engine ; the 
stem r of the handle passes through the moveable 
disk, and enters the other in its centre, so as to 
keep both in a right position over each other. In 
fig. 32, these two disks are distinguished from each 
other by hatchings running different ways. By 
moving the superior disk K, with the handle T, 
circularly on the inferior disk, the two apertures 
may be brought to correspond exactly with each 
other, as in fig. 32, and then the passage is entirely 
open. If only partially moved, as represented by 



i 



DESCRIPTION. 27 

the dotted lines in fig. 33, the passage is only 
partially opened; and when the two apertures do 
not correspond at all, the communication is com- 
pletely intercepted : when the passage is thus shut, 
it is the steam itself that keeps the two disks in 
immediate contact with each other, by pressing 
with all its force on the superior disk. 

Tins regulator may also be constructed in a dif- 
ferent way. It is sometimes made in the form of a 
common two-way cock, the steam coining from 
above ; but the one described above is most com- 
monly used. 

Sbct. XL Of the Joints or rubbing parts. 

In aU the joints of any importance the oil is fed 
without interruption by means of a cup, with a wick- 
syphon placed above the joint, as in fig. 35, Plate II. 
This cup is made in the form of a school-boy's ink- 
horn, so that the velocity of the motion may not 
spill the oil ; and there is at the bottom of it a small 
tube, penetrating to the entrance of the joint. A 
cotton-wick dipping in the oil of the cup passes 
into the tube, and, sucking continually the oil out of 
the cup, drops it into the joint without interruption. 

Sect. XII. Of the Fire-grate. 

The grate in the fire-place is not made of a single 
piece. It is formed of separate bars, which are 



28 CHAPTER I. 

placed side by side at the bottom of the fire-place, 
where they are' supported at their two ends. The 
advantage of this arrangement is the fistcility it 
affords of replacing the bars individually by new 
ones, when they are worn out by the intensity of the 
fire. Besides, if any accident should happen to the 
boiler, and make the water run off unexpectedly, 
thus endangering the engine, the engine-man may, 
by means of a hook, easily turn the bars upside 
down, and consequently extinguish the fire immedi- 
ately by letting it fall on the road, with the bars 
that supported it. It is also thus that every even- 
ing the fire-place is emptied, after the engine has 
finished its work. 



Sect. XIII. Of the disposition of the different parts. 

We shall complete this description by showing 
on the whole engine, as represented in figs. 1,2, and 
3, the places occupied by the different parts of 
which we have spoken. 

A, Part of the boiler containing the fire-place. 
BB, Stand for the engine-man and his assistant. 

C, Chinmey of the engine. 

D, Place of the cylinders. 

E, First safety-valve, with lever and spring balance, 

as will be explained hereafter. 

F, Second safety-valve, constructed in the same 

manner. 

G, Glass-tube. 



DESCRIPTION. 29 

Hy Gauge-cocks. 

I, End of the eccentric-rod. 

J, Horizontal guides for the head of the piston- 
rod, so as to ensure its motion in the exact 
direction of the axis of the cylinder. 

K, Cross-axle, communicating the motion of the 
eccentric-rod to the slide-rod, by means of 
the arms KU and K t, which are fixed upon 
it. (See figs. 9 and 10.) 

h\ Notch for throwing in gear the eccentric-rod 
with the cross-axle which works the slide- 
rods. 

MM, Rod by means of which the engine-man can 
raise the eccentric-rod, and throw it out of 
gear with the cross-axle which works the 
shdes. This is performed by means of the 
arms m and m' connected together. When 
the engine-man pulls the rod MM, he causes 
the arm m' to rise, and with it the small rod 
m'o\ which lifts the eccentric-rod out of gear 
with the arm KU. 

N, Handle, by means of which the engine-man 
pulls the rod MM, so as to produce the 
aforesaid effect. 

PP, Handles to move the slides when they are 
thrown out of gear with the eccentrics. The 
handles acting upon the cross-axle Q, move 
the cross-heads RR, which are fixed to it. 
This motion is communicated by means of 



30 CHAPTER I. 

the rods SS to the cross-heads rr^ which act 
upon the axle working the sUdes. 

Ty Handle of the regulator, to open more or less 
the aperture through which the steam passes 
from the boiler to the cylinders. 

V, Steam dome, in which the steam is confined 
till it can escape through the aperture of 
the regulator, and penetrate into the cy- 
linders. 

U, Man-hole, or aperture closed by a strong iron 
plate, and large enough to admit a man into 
the boiler, when necessary. 

XXX, Iron knees, by which the boiler is fixed to 
the fi'ame of the carriage. 

ZZy Springs resting at oa on the chairs of the 
wheels, by means of two vertical pins pass- 
ing through holes in the frame of the engine. 
One end of the pin resting on the back of 
the spring, and the other on the upper 
side of the chair, the whole weight of the 
machine is thus supported by the wheels, 
but through the intermediate action of the 
springs. 

bhy Guides for the chair of the wheel to slide up 
and down, according as the spring bends 
more or less under the weight of the engine. 
The upper part of the chair is scooped out 
to form a small reservoir for oU. This reser- 
voir, as well as those above mentioned, con- 



DBSCRIPTION. 31 

tains a tube and a syphon-wick, for feeding 
constantly the oil upon the axle, at its rub- 
bing point with the axle-box. 

Cy Suction-tube, by which the feeding-pump draws 
the water from the tender, to transmit it to 
the boiler. This tube is afterwards continued 
by another flexible tube made of hemp cloth, 
but supported within by a spiral spring, 
and through which the water arrives from 
the tender to the pumps of the engine, when 
a cock fixed to the tender is opened. 

p, Feeding-pump of the engine, which is con- 
stantly set in motion by a connexion with 
the piston-rod of the corresponding cylinder, 
but which cannot force any water into the 
boiler, unless the cock which lets the water 
come in from the tender be opened. 

p\ Handle and rod of the safety-cock of the pump, 
serving to ascertain whether the water really 
arrives in the cylinder of the pump. This 
cock leads without, so that when it is open 
and the pump is working, a small jet of 
water may be seen issuing from it, which 
shows that the pump has its proper effect. 

ee. Buffers, or pads stuffed with horse-hair, to 
deaden the shocks which may be given or 
received by the engine. Their elasticity is 
sometimes augmented by means of a spiral 
spring within them. 

/, Cock, by means of which the water which is 



32 CHAPTER I.' 

sometimes carried from the boiler to the 
cylinder may be let out. 

g, Mud-hole, or opening made in the double 
casing of the fire-box and closed with a 
screw-bolt. In withdrawing this bolt, a 
cleaning-rod may be introduced into the 
double casing ; and, by means of a forcing- 
pump, water may be injected with force, 
to cleanse out the clay sediment left by the 
boiling of the water. This cleaning is usually 
performed once a week. 

A, (fig. 3.) Moveable plate or door of the smoke- 
box ; by opening which, the ends of the tubes 
of the boUer, the cylinders, the slides, and the 
steam-pipes leading from the boiler to the 
slide-boxes, or froxcL the slide-boxes to the 
chimney, are visible. This door is opened 
when it is necessary to regulate the slides, 
as we shaU see hereafter. 

i. Whistle, by means of which the engine-man 
announces at a distance the arrival of the 
engine. It consists of a sort of inverted 
tumbler, against the edge of which, on turn- 
ing a cock, the steam is directed. The 
forcible rush of this causes a sound nearly 
like that of a boatswain's call. This whistle 
is also represented fig. 25. 



DESCRIPTION. 33 



ARTICLE II. 

OP THE PRINCIPAL DIMENSIONS OF THE ENGINES. 

Sect. I. Of the dimensions of the parts from which 
the power of the engine is derived. 

The foregoing description applies to the most 
modem locomotive engines, such as those we used 
for our experiments. But to give a more complete 
idea of them, we must say something of their prin- 
cipal dimensions. 

Locomotive engines may be constructed of all 
sizes and proportions, according to the road on 
which they are to move and the work to which they 
are destined. But to show the dimensions that 
have hitherto been most generally employed, we 
will give those of the locomotives of the Liverpool 
and Manchester Railway, remarking at the same 
time, that the engines most frequently constructed 
now are those of the largest dimensions, and that 
the engines having cylinders of 8 or 10 inches 
diameter are only remains of the old engines of the 
C!ompany. ' The Liverpool and Manchester Rail* 
way is 4 feet 8^ inches wide from rail to rail, 
and the velocity does not exceed 30 miles an hour. 
For railways of greater width, and whereon a greater 
velocity is intended, engines of larger dimensions 
have been constructed. The following Table then 
is not to be regarded as Umiting the dimensions of 
locomotives, but as intended merely to complete the 

D 



34 



CHAPTER I. 



foregoing description, by making known the most 
usual proportions, and particularly those of the 
engines used in the experiments contained in this 
work. 



Dimensions of the Locomotive Engines on the Liverpool and 

Manchester Railway (1836). 



Number 


Diameter 




Diame- 


Weight of 


Effective pressure 


of en- 


of the 


Stroke of 


ter of the 


the 


in the boiler, in lbs 


gines. 


cylinder. 


the piston. 


wheel. 


engine. 


per square inch. 




inches. 


inches. 


feet. 


tons. 


lbs. 


2 


8 to 10 


17 and 16 


5 


7 to 8 


50 


9 


11 


16 


5 


8 to 9 


50 


6 


11 


18 


5 


10 to 12 


50 


2 


11 


20 


5 


11 to 12 


50 


2 


12 


16 


5 


11 to 12 


50 


2 


12 


18 


5 


12 to 12i 


50 


5 


12i 


16 


5 


10 to 11 


50 


1 


14 


12 


5 


Hi 


50 


2 


14 


16 


5 


12 


50 


2 


15 


16 


5 


12i 


50 



Most of these engines have now six wheels, 
two of which, five feet in diameter, are worked 
by the steam, and four, three feet in diameter, 
are destined merely to sustain the weight of the 
engine. Sometimes the six wheels are of equal size, 
and are all set in action by the steam, by means 
of connecting-rods which conununicate the motion 
of the driving-wheels to the four others. The ad- 
vantage of this last disposition is to make the engine 
adhere to the rails by six wheels instead of two ; but 
a very ingenious apparatus, invented by Mr. John 



DESCRIPTION. 35 

Melling, foreman of the Company's factory at Liver- 
pool, and of which we shall speak hereafter in 
Chapter XIV., allows the same advantage to be 
obtained with wheels of unequal diameter ; which 
besides are more favourable to the convenient ar- 
rangement of the divers parts of the engine. 

The end proposed in adopting six wheels rather 
than four is to lessen the wear and tear of the rails 
by dividing the weight of the engine among six 
supports instead of four. A second motive also is 
in view ; namely, to prevent all possibility of acci- 
dent in the event of the crank-axle happening to 
break. In this case a four-wheel engine would run 
the risk of going off the rails, but if supported on 
six wheels the remaining four will necessarily keep 
it on the line. 



Sect. II. Dimensions of the fire-box and boiler of 
some of the best engines of the Liverpool and 
Manchester Railway. 

m 

It is from the dimensions we have just noticed, 
and more especially from those of the cylinder and 
stroke of the piston, that the power of locomotive 
engines is generally expressed. It will appear, how- 
ever, in the course of this work, that for such 
expression of the power to be complete, and really 
sufficient to give the effect of the engine under 
all circumstances, the evaporating power of the 
engine, or, which amounts to the same, the heating 



36 CHAPTER I. 

surface of the boiler, ought to be considered also. 
Without this principal element, an expression of 
the power of a steam engine is mere illusion. 

In the fire-box and boiler resides, in fact, the real 
source of the effects of the engine : the cylinder 
and other parts are the means of transmitting and 
modifying the power ; but what could be their use, 
if that power itself did not exist ? 

To complete, therefore, the proportions already 
given above, we shall add here a Table of the di- 
mensions of the fire-box and boiler in the different 
engines to which we shall have occasion to refer. 
In another part of the work, our experiments will 
enable us to replace this complex datum by the 
simple expression of the evaporating power of those 
engines. The two most important columns of this 
Table are those which show the extent of surface 
exposed to^the action of the caloric, whether radi- 
ating or communicative. 

We introduce the engines in the order of the dates 
of their construction. The two engines Goliath and 
Fire-fly bear the number 1 , because it will be seen 
farther on, in Chapter X., that in rebuilding those 
engines, boilers were adapted to them different from 
those which they had originally, that is to say, dif- 
ferent from those which appear in this Table ; an(( 
therefore we shall have to distinguish these new 
boilers by the number 1 1 . 



DESCRIPTION. 



37 



O 
O 

I 



«5 



^^is? 



its 






fl O V tt s 

»^ ^ ** ♦• ^ 



1^1 



SsSS 








0000 
10 to to to 



O 
«o 



•9 

u 01 C9 01 CO CO CO (N ^ 



0000 
to 10 U3 u> 

• • • « 

00 CO CO 00 01 



"S t^ C9 t^ ^ eo 



00 

• • • 

.§0^0 

9 



t^ CO G4 

•* O t^ 

^_ • • ■ • 

00 i-H 00 "-^ w 



00 



C4 00 o c« 

CO <N 00 CO 

• • • • 

00 00 <^ O 



OOdt^Oco i-H ooo)<o;o 

00 CO <o r^ t^ 



9*^ ^ r^ CO CO CO O) t^ 



\^ t<^ooooco^C9co 01 r^oot^^ 

^ t^ t>.»r3t^t^C4t^»o CO (NCN»r>^o) 

0«t^ OiOCOCOlAO)^ rl* OCOi-iC^ 

• 00 ^OOC9CIC4^G4 CSI C4CS|C0<N 






;0 i-i to t^ CO CO 

O 00 Tf 00 CO o 

« • 

CO O 

00 tJ* 



^ CT tN, r*. CO 

CO CO 00 kO <^ 



CO <^ t^ ^ r-i 

CO CO to o) r^ 

• • • • • 

O) C9 -^ 00 O) 

CO CO CO -^ -^ 



gr<»r<%t^t^CN»r<%r^r<%OC^kOt^t^t^ 

^^^^<^^^^^coc^OO^Tt*rl* 



§ 



O t^ 
OiOir^t^t^»oO j^ oor^o<N 

t>»COOOO)COOO O) COO<-iO) 



Length 
of the 
boiler 


na ^ 


1 















«o 


00 







CO 








00 


a| 


4^ 


tea 

• 

CO 


r* 


• 

CO 


CO 


• 

CO 


00 

• 


t^ 


• 

CO 


CO 

• 

CO 


(0 


«o 

• 


00 

• 

4^ 




• ^ 


i 





10 













uo 




to 






00 


3 •« 


JSS 


>o 


t^ 


>o 










t^ 




t^ 









s^ 


-i 


«S 


00 


Cil 


CO 


oo 


CO 


00 


CO 


Cil 


00 


(N 


oo 


00 


00 



r 



S S d 

45 ^^ ^wm 



^ 



T*5 I 



6 

'G) 
S 






^CO COCOCOCOCOCOCO CO Q0CO00G4 

^^^ ^ ^ ^ ^ ^ >,, ^ ^ ^ ^ ^ ^ 

•• *••••••• « 

agg^-g 5- 



i 



38 CHAPTER I. 

It wUl be seen hereafter, that, with a boiler of 
those dimensions and of such a form, the engines 
are able to evaporate about a cubic foot of water 
per minute, or a poimd of water per second, at the 
effective pressure in the boiler of 50flbs. on the 
square inch. 

Sect. III. Of the old Locomotive Engines, 

The description given above is applicable to 
engines intended for great speed, and particularly 
for the conveyance of passengers. That form is 
exclusively adopted in all modem railways. 

On some lines, however, engines of another con- 
struction are to be foimd. The railway from Stock- 
ton to DarUngton being used for a different service, 
that is to say, for the conveyance of coals and for a 
more moderate velocity, it may be proper to give 
here an idea of the engines used on that line. 

Those engines are of different models, from the 
oldest to the most recent ones. 

In some the fire passes through the boiler 
in a single tube, which serves as a fire-place, 
and communicates directly with the chimney. In 
some others the tube bends round in the boiler 
before it reaches the other end, and comes back 
to the chimney, which, in that case, is placed 
next to the door of the fire-place. In others, the 
tube or flue, when it reaches the end of the boiler, 
divides and returns towards the chimney, as two 
smaller tubes. . In some, the fire being still placed 



DESCRIPTION. 39 

in an internal flue, the flame returns to the chimney 
by means of about 100 small brass tubes, on a 
principle similar to that of the Liverpool engines. 
Lastly, three of them are constructed on the same 
model as those of Liverpool. 

The Company carries both passengers and goods. 
The first travel with a speed of twelve miles, and 
the second of eight miles, an hour. Of the different 
forms of boilers, those only with a set of small tubes 
suit for carrying passengers; the others cannot 
generate a sufficient quantity of steam for the ve- 
locity wanted. But when a speed of eight miles per 
hour only is required, the most convenient boilers 
have been found to be those with one returning 
tube. They generate a sufficient quantity of steam 
for the work required of them, and have the ad- 
vantage of being cheap in regard to prime cost and 
repairs, as their form is simple, and they are entirely 
made of iron, whilst the tube boilers require the use 
of copper. 

Besides the difference in the form of the boilers, 
the other parts of the engine differ also. The 
cylinders are placed on the outside, and in a ver- 
tical position. The motion is not communicated 
from the piston to the engine by a crank in the axle, 
but by a rod working outside of the wheel, and 
resting upon a pin fixed in one of the spokes. Those 
engines have in general six equal wheels, of four feet 
diameter. Two of the wheels are worked by the 
steam, as has been just explained ; and the four 



40 



CHAPTER I. 



others are attached to the former by connecting- 
rods, which cause them to act all together. 

The weight of these engines varies. Setting aside 
those which we have mentioned as being on the 
model of the Liverpool ones, and which are very 
light, the average weight of the others is from ten 
to twelve tons. 

All these engines are supported on springs. In 
some of the older ones, the water of the boiler, 
pressing upon small moveable pistons, and pressed 
itself by the steam contained in the boiler, was 
intended to supersede the springs; but though 
that system displayed a great deal of ingenuity, 
the spring it formed was found in practice to be 
too variable, and the system was given up. 

The usual proportions adopted for the engines on 
that railway are the following : 



Cylinder 


# • ■ 


14|^ inches. 


Stroke 


• • 4 


. 16 — 


Wheels 


• ■ 


4 feet. 


Weight 


• • 


11 tons. 


Eifectiye 


pressure . 


48 lbs. per square inch 



The pressure, however, varies according to the 
ascertained solidity of the boiler. When the sheets 
of which it is formed begin to grow very thin, the 
pressure is sometimes reduced to 36fts. only per 
square inch; in other circumstances, it is, on the 
contrary, increased to J60 fts. 



CHAPTER II. 

OF THE LAWS WHICH REGULATE THE MECHANI- 
CAL ACTION OF THE STEAM.^ 

Sect. I. Relation between the temperature and the 
pressure of the steam in contact with the liquid. 

Bbfobb entering upon considerations which have 
for their basis the effects of the steam, it may be 
necessary to lay down, in a few words, some of the 
laws according to which the mechanical action of 
the steam is determined or modified. 

In the calculation of steam engines it is requisite 
to consider four things in the steam. 

Its pressure^ which is also called tension or 
elastic force, and which is the pressure it exerts 
on every unit of the surface of the vessel that con- 
tains it. 

Its temperature, which is the number of degrees 
marked by a thermometer immerged in it. 

Its density, which is the weight of a unit of its 
volume. 

' Thifl chapter has already appeared in the work entitled 
" Themy of the Steam Engine" hat we deem it convenient to 
give the greater part of it here also, that the reader may not he 
ohliged to recur to another work. 



42 CHAPTER II. 

And its relative volume^ which is the volume of 
a given weight of steam compared to the volume of 
the same weight of water, or, in other words, to 
the volume of the water that has served to produce 
it. We deem it necessary to add here the word 
relative, in order to avoid the confusion which would 
otherwise arise continually between the absolute 
volume filled by the steam, which may depend on 
the capacity of the vessel that contains it, and the 
relative volume which is the inverse of the density. 
Thus, for instance, steam generated under the 
pressure of the atmosphere may fill a vessel of any 
size, but its relative volume will always be 1700 
times that of water. 

When the volumes occupied by the same weight 
of two different steams are compared together, it 
is evidently a comparison of what we call the rela- 
tive volumes of those two steams. For, the two 
steams compared having the same weight, corre- 
spond to the same volume of water evaporated. 
Therefore it follows that the ratio of the relative 
volumes of the two steams is the same as the ratio 
of their absolute volumes. 

To make this more clear, if S express a given 
volume of water, M the absolute volume of the steam 
resulting from it under a certain pressure p, and M^ 
the absolute volume of the steam which results from 
it under another pressure p\ the relative volume of 
the steam under the pressure p, which relative 
volume we will express by /i, will be 



OF THE MECHANICAL ACTION OF THE STEAM. 43 

M 

and the relative volume of the steam uiider the 
pressure p , which relative volume we will express 
' by /, will be 

'^ s 

I Consequently will be deduced 

/i M 

i 

A* 



' M'^ 



that is to say, the ratio between the absolute 
volumes occupied by like weights of two different 
steams, is, as we have said, nothing more than the 
ratio between the relative volumes of those steams. 

These definitions premised, the steam may be 
considered at the moment of its generation in the 
boiler, when still in contact with the liquid from 
which it emanates, or else as being separated from 
that liquid. 

When the steam, after having been formed in 
a boiler, remains in contact with the generating 
water, it is observed that the same temperature 
corresponds invariably to the same pressure^ and 
vice versd. It is impossible then to increase its 
temperature, without its pressure and density in- 
creasing spontaneously at the same time ; and it is 
impossible also to increase its density or its pressure, 
except by increasing at the same time its tempera- 
ture. In this state the steam is therefore at its 



44 CHAPTER II. 

maximum density and pressure for its temperature^ 
and then a constant connexion visibly exists be- 
tween the temperature and the pressure. 

If on the contrary the steam be separated from 
the water that generated it, and that the tempe- 
rature be then augmented, the state of maximum 
density will cease, since there will be no more water 
to furnish the surplus of steam, or increase of den- 
sity, corresponding to the increase of temperature. 
That invariable connexion above mentioned, between 
the temperature and the pressure, will then no longer 
exist, and, by accessory means, the one may at 
pleasure be augmented or diminished, without any 
necessity of a concomitant variation taking place in 
the other, as it happens in the case of the maximum 
density. 

It is necessary then to distinguish between these 
two states of the steam. 

One of the most important laws on the properties 
of steam is that which serves to determine the 
elastic force of the steam in contact with the liquid, 
when the temperature under which it is generated 
is known ; or, reciprocally, to determine that tem- 
perature when the elastic force is known. Not only 
is this inquiry of a direct utility, but we shall see 
in the sequel that it serves equally to determine the 
density or the relative volume of the steam formed 
imder a given pressure, a point of knowledge in- 
dispensable in the calculation of steam engines. 

Experiments on this subject had long been taken 



OF THE MECHANICAL ACTION OF THE STEAM. 45 

in hand, and they were very numerous for steam 
formed under pressures less than that of the atmo- 
sphere ; but for high temperatures, the experiments 
extended but to pressures of four or five atmo- 
spheres. Some few only went as far as eight, and 
that without completing the scale in the interval. 
The extreme difficulty of researches of this kind, if 
it be desired to attain results really exact, the heavy 
expenses they occasion, and the danger attending 
them, had prevented the experiments from being 
carried farther. But to the Academy of Sciences of 
the Institute of France we are indebted for a com- 
plete Table on this subject. The Academy confided 
the conduct of these delicate experiments to two 
distinguished scientific men, Messrs. Arago and 
Dulong, who evinced in them every nicety that 
a perfect knowledge of the laws of natural phi- 
losophy could suggest, to avoid the ordinary causes 
of error. Never were researches of this kind con- 
ducted on so vast a scale, nor with more accuracy. 
The pressure of the steam was measured by^ effective 
columns of mercury contained in tubes of crystal 
glass, which together extended to the height of 87 
feet English. The instruments were constructed by 
the most skilful makers, and no expense was spared.^ 



^ Vide Expos^ des recherches faites par ordre de T Acad^ie des 
Sciences, poar determiner lea forces ^astiques de la vapeur d'eau 
ii de hautes temperatures. Mhunres de TAcadhnie des Scienceg, 
tome X. ; Annales de Chimie et de Physique, tome xliii. 1830. 



46 CHAPTER II. 

Therefore the greatest degree of confidence is to be 
attached to their results. 

These beautiful experiments furnish a complete 
series of observations, from the pressure of 1 atmo- 
sphere to that of 24. To form, however, a Table 
extending beyond this limit, Messrs. Dulong and 
Arago have sought to deduce from their observa- 
tions a formula which might represent temperatures 
for still higher pressures without any noticeable 
error. They have in fact attained that end, by 
means of a formula which we shall presently report, 
and whose accord with experience is such, for all 
that part of the scale above four atmospheres, as to 
give room to think that, on being appUed to pres- 
suiea up to 50 atmospheres, the error in tempera- 
ture would not in any case exceed 1 degree of the 
centigrade thermometer, or 1*8 degree of Fahrenheit. 
They were enabled then, as well from the result of 
their observations as by means of an amply justified 
formula, to compose a Table of temperatures of 
steam up to 50 atmospheres of pressure, with, the 
certainty of committing no error worthy of note. 

Though the formula of Messrs. Arago and Dulong 
may be applied to pressures comprised between 1 
and 4 atmospheres, with an approximation that 
would suffice for most of the exigencies in the arts, 
they did not indicate the use of it for that interval, 
because in that part of the scale other formulas 
already known accord more exactly with the results 
of observation, and ought, in consequence, to be 



OF THE MECHANICAL ACTION OF THE STEAM. 47 

preferred. Among those formulse, that originally 
proposed by Tredgold, and afterwards modified by 
his translator, M. Mellet, gave the most exact 
results ; and no inconvenience arises from the use 
of it, when it is required merely to compose a Table 
by intervals of half-atmospheres. But as, for the 
more commodious use of the formulae which we have 
to propose in this work, we shall want to establish a 
Table by intervals of pounds per square inch ; we 
deem it better to employ a formula which we shall 
give with the others presently, and which, approach- 
ing as near as that of Tredgold to the results of direct 
observation, in the points furnished by experiment, 
has moreover the advantage of coinciding exactly 
at 4 or 4^ atmospheres with the formula of Messrs. 
Dulong and Arago, which is to form the continu- 
ation of it.^ 



^ In fact, comparing, in French measure, the two formulae with 
the observation, we find the following results, as it will be easy to 
verify hereafter! 



Elastic force 
of the steam 
in atmo- 
spheres. 


Observed 
temperature, 
by the centi- 
grade ther- 
mometer. 


Temperature 
given by Tred- 
gold's formula, 

modified by 
MeUet. 


Temperature 
given by 

the proposed 
formula. 


Temperature 

g^ven by the 

formula of 

Messrs. Arago 

and Dulong. 


1 


100 


99-96 


100 


»» 


214 


123-7 


123-54 


123-34 


99 


2-8705 


133-3 


133'54 


13317 


»t 


4 


»* 


145-43 


144-88 


tf 


4-5735 


149-7 


150-39 


149-79 


149-77 



It appears that the formula which we propose difiers from the 



48 CHAPTER II. 

These formulae, as well as other similar ones, 
have the inconvenience of suiting only a limited part 
of the scale of temperatures. 

Among the formulae proposed by different authors 
on the same subject, that of Southern is very suit- 
able to steam formed xmder pressures inferior to that 
of one atmosphere ; it deviates then from the truth 
only in very low pressures, as appears from the 
experiments of that engineer. But for pressures 
superior to 1 atmosphere it ceases to have the same 
accuracy : from 1 to 4 atmospheres it gives, in fact, 
more error than that of Tredgold modified, and 
above 4 atmospheres the error rises rapidly to 1 and 
1 '5 degree of the centigrade thermometer, or 1*8 and 
2*6 degrees of Fahrenheit ; so that the formula of 
Messrs. Arago and Dulong, which is, besides, of 
more easy calculation, becomes then far preferable 
to it. 

That of Tredgold modified, as well as that which 
we propose to substitute for it, represent very 
closely the observations for the interval between 
1 and 4 atmospheres; but below that point they 
are incorrect, and above it they are inferior in 
point of accuracy to that of Messrs. Dulong and 
Arago. 

The latter accords remarkably well with the facts. 



observed temperatures nearly as much as that of Tredgold modi- 
fied ; but as the difierence from the observation is on the mtmw 
side instead of the pkts, there results a coincidence at 4^ atmo- 
spheres with that of Messrs. Arago and Dulong. 



OF THE MECHANICAL ACTION Of THE STEAM. 49 

from 4 atmospheres to 24. In this interval its 
greatest difference with observation is -4 degree 
of the centigrade thermometer or '7 of Fahrenheit, 
and nearly all the other differences are only * 1 de- 
gree centigrade or '18 Fahrenheit ; but, as we have 
already said, it begins to deviate from the obser- 
vation below 4 atmospheres. 

No one, then, of these formulae suits the whole 
series of the scale of temperatures, and to hold 
exclusively to any one of them would be knowingly 
to introduce errors into the Tables. As, moreover, 
the true theoretic law which connects the pressures 
with the temperatures is unknown, and as these 
formulae are mere formulae of interpolation, esta- 
blished solely from their coincidence with the facts, 
the only right mode of making use of them is to 
apply each respectively to that portion of the series 
which it suits. Then, from the comparison of their 
results with experience, one may rest assured that 
the error on the temperature will in no point exceed 
seven-tenths of a degree of Fahrenheit, or four- 
tenths of a degree of the centigrade thermometer. 
This is, therefore, the means we shall adopt in the 
formation of the Tables we are about to present. 

The formulae, which will serve to compose these 
Tables, are then the following, which we present 
here, not in their original terms, but transformed, 
for greater convenience, into the measures usual 
in practice ; that is, expressing the pressure p in 
pounds per square inch or in kilograms per square 

B 



50 CHAPTER II. 

centimetre, and the temperature ty in degrees of 
Fahrenheit's, or of the centigrade thermometer, 
reckoned in the ordinary manner. 

Southern's formula, suitable to pressures less 
than that of the atmosphere (English measures): 

<=1557256 */y/|i- 04948-51 -3. 

Tredgold's formula modified by M. Mellet, suit- 
able to pressures from 1 to 4 atmospheres (English 
measures) : 

_/103+^\« 
^ V20118>' ' 

<=201- 18/^11-103. 

Proposed formula, suitable like the preceding, to 
pressures from 1 to 4 atmospheres (English mea- 
sures): 

_/98^806-M\« 
^ V 198-562 ^ ' 

<= 198-562 /^|i-98-806. 

Formula of Messrs. Dulong and Arago, suitaUe 
ta pressures from 4 to 50 atmospheres (English 
measures) : 

;)=(-26793-f 0067585 <)*, 

<= 147-961 /^p-39-644. 

Southern's formula, suitable to pressures less 
than that of the atmosphere (French measures) : 



OF THE MECHANICAL ACTION OF THE STEAM. 51 

^=145-360*^1?- 0034542— 46-278. 

Tredgold'8 fonnula modified by M. Mellet, suit- 
able to pressures of 1 to 4 atmospheres (French 
measures) : 

^=174 /(/p- 75. 

Proposed formula, suitable like the preceding, to 
pressures from 1 to 4 atmospheres (French mea- 
sures) : 

_x 72-67+< y 
^ V 171 72 ^ ' 

^= 171-72 y^p-72-67. 

Formula of Messrs. Dulong and Arago, suitable 
to pressures from 4 to 50 atmospheres (French 
measures) : 

p= (•28658+0072003 <)*, 

t= 138-883 /^-39-802. 

Besides the formulae which we have just re- 
lated, there exists another proposed by M. Biot, 
which, compared by that illustrious natural phi- 
losopher to the above-mentioned experiments on 
high pressures, to those of Taylor on pressures 
approaching nearer to 100 degrees centigrade, and 
to a numerous series of manuscript observations 



K 



i>2 CHAPTBR II. 

made by M. Gay-Lussac, from 100'' to — 20 de- 
grees centigrade, reproduces the results observed, 
with very sUght accidental deviations, such as the 
experiments themselves are liable to. This formula, 
which has consequently the advantage over the 
preceding, of being appUcable to all points of the 
scale, is the following :--- 

log. p=a-a,6.'*'*'-a,6,"^'. 
Log. p is the tabulary logarithm of the pressure 
expressed in millimetres of mercury at 0° centi- 
grade ; / is the centesimal temperature counted on 
the air thermometer, and the quantities a, a,, a,, b,, 
bf, are constant quantities which have the following 
values: 

a - 5-96131330259, 

log. a,= T-82340688193, 

log. 6,= --01309734295, 

log. o.= 74110951837, 

log. 6,= -00212510583. 

This formula cannot tail to be extremely useful 

in many delicate researches on the effects of steam ; 

but to establish, by its means, a Table of the form 

we require, the pressure ought first to he deduced 

from it for each degree of the air thermometer ; 

then these degrees ought to be afterwards changed 

into degrees of the mercury thermometer ; and as 

Hiia would not give the temperatures corresponding 

to given pressures, by regular intervals, a subsequent 

nterpolation would be still necessary to make the 

Table in the proper disposition. These long opera- 



OF THE MECHANICAL ACTION OF THE STEAM. 53 

tions induced us to give the preference to the pre- 
viously cited formulae, for the construction of the 
Tables which we shall shortly present. 

Sect. II. Relation between the relative volumes 
and the pressures, at equal temperature, or be- 
tween the relative volumes and the temperatures, 
at equal pressure, in the steam separated from 
the liquid. 

We have said that when the steam is in contact 
with the generating liquid, its pressure is neces- 
sarily connected with its temperature; and as the 
density of an elastic fluid depends only on its 
temperature and its pressure, it follows that the 
density is then always constant for a given tem- 
perature or pressure. But when the steam is 
separated from the liquid, that connexion between 
the temperature and the pressure no longer exists. 
The temperature of the steam may then be varied 
without changing its pressure, or reciprocally ; and 
according as the one or the other of these two 
elements is made to vary, the density of the steam 
undergoes changes which have been an object of 
investigation among natural philosophers. 

One very remarkable law in the effects of gas 
and steam is that which was discovered by Mariotte 
or Boyle, and has since been confirmed, as far 
as to pressures of 27 atmospheres, by Messrs. 
Arago and Dulong. It consists in this, that if the 



54 CHAPTER II. 

volume of a given weight of gas or of steam be 
made to vary without changing its temperature, 
the elastic force of the gas will vary in the inverse 
ratio of the volume it is made to occupy ; in other 
words, in direct ratio of its density. That is to say, 
if V and t/ express the volumes occupied by the 
same weight of steam, and p and p' the pressures 
which maintain the steam compressed under those 
respective volumes, the temperature, moreover, 
being the ^ame in both cases, the following analogy 
will exist : 

p ^v 

"7 *" "~' 

p V 

And therefore, fi and ^' being the relative volumes 
of the steam at the pressures p and p\ we shall have 

p lu 

According to this law, if a given weight of an 
elastic fluid be compressed to half its primitive 
volume, without changing its temperature, the 
elastic force of that fluid will become double. But 
it is plain that this efiect cannot take place in the 
steam in contact with the liquid, because it supposes 
that during the change of pressure the temperature 
remains constant, whereas we have seen that in 
such state, the pressure always accompanies the 
temperature, and vice ^ersA, 

Another property equally important in the ap- 



OF THE MECHANICAL ACTION OF THE STEAM. 55 

predation of the effects of steam has been discovered 
by a celebrated chemist of our times, M. Gay- 
Lussac. It consists in this, that if the temperature 
of a given weight of an elastic fluid be made to vary, 
its tension being maintained at the same degree, 
it will receive augmentations of volume exactly 
proportional to the augmentations of temperature ; 
and, according to the latest experiments, for each 
degree of the centigrade thermometer, the increase 
of volume will be '00364 of the volume which the 
same weight of fluid occupies at the temperature 
zero. If the temperatures are taken from Fahren- 
heit's thermometer, each augmentation of 1 d^^ree 
in the temperature will produce an increase of 
'00202 of the volume occupied by the fluid at the 
temperature of 32°. 

K then we call V the volume of the given weight 
of the elastic fluid, under any pressure, and at the 
temperature of 32 degrees of Fahrenheit, the volume 
it will occupy under the same pressure, and at the 
temperature t of Fahrenheit, will be 

i;=V+Vx 00202 (^-32). 

It follows that, between the volumes, v and v 
occupied by the same weight of steam, at the same 
pressure and under the respective temperatures 
t and t\ there will be the following analogy : 

t;_ 1+00202 U-32) 
»'" 1+00202 U'-32)* 



56 CHAPTER 11. 

And since we have seen that the ratio between the 
volumes occupied by the same weight of two dif- 
ferent steams is no other than the ratio between 
the relative volumes of those two steams, the two 
preceding analogies will also be true, when we 
replace the ratio of the two absolute volumes t; and 
Vy by the ratio of the relative volumes ii and fi of 
the steam. 

This law, supposing that the temperature of the 
steam changes, without the pressure undergoing 
any change, obviously cannot apply to the effects 
produced in steam in contact with the liquid, since 
in such steam the pressure changes necessarily and 
spontaneously with the temperature. 

Sect. III. Relation between the relative volumes^ 
the pressures^ and the temperatures^ in the steam 
in contact or not in contact with the liquid. 

As it has just been observed, neither Boyle's 
law nor that of Gay-Lussac can apply alone to 
changes which take place in the steam remaining 
in contact with the liquid. But it is clear that 
from the two a third relation may be deduced, 
whereby to determine the variations of volume 
which take place in the steam, by virtue of a 
simultaneous change in the temperature and in 
the pressure; and this relation may then com- 
prehend the case of the steam in contact with the 



OF THE MECHANICAL ACTION OF THE STEAM. 57 

liquid, since it will suffice to introduce into the 
formulae the pressures and temperatures which, 
in this state of the steam, correspond to each 
other. 

Suppose then it be required to know the volume 
occupied by a given weight of steam, which passes 
from the pressure |>' and temperature t\ to the 
pressure f and temperature t. It may be supposed 
that the steam passes first from the pressure 'p' to 
the pressure p without changing its temperature, 
which, from Boyle's law, will give between the 
relative volumes of the steam the analogy 

/^ =/* -; 
V 

then supposing this steam to pass from the tem- 
perature i to the temperature f, without changing 
its pressure, the relative volume of the steam, ac- 
cording to the law of Gay-Lussac, will become 

_ // I +00202 (^-32) _ 
^ ^ 1+00202 {i—2fl) 

_ ,/ 1+00202 (^--32) 
^p' 1+00202 (<'-32)' 

This formula will then express the law according 
to which the relative volume of the steam changes, 
by virtue of a given combination of pressure and 
temperature. Consequently, substituting in this 
equation for f and ^, f' and t\ the pressures and 
temperatures only which correspond to each other 



58 CHAPTER II. 

in the steam iii contact with the liquid, we shall 
have the analogous changes which take place in 
the relative volume of the steam, when it is not 
separated from the water which generated it. 

On the other hand, it is known by experience, 
that under the atmospheric pressure, or 14*706 9bs. 
per square inch, and at the temperature of 212° of 
Fahrenheit's thermometer, the relative volume of 
the steam in contact with the liquid is 1700 times 
that of the water which has produced it. Hence 
it is easy to conclude the relative volume of the 
steam at any given pressure p and at the corre- 
sponding temperature t. It suffices, in fact, to 
insert the above values for p\ f^ and /, in the 
general equation obtained above, and the result 
will be 

,„i700x. 14706 1+00202 (t^32) _ 
^ p ^1+00202x180 

= 18329 1+00202 (<--32) 

P 

Thus we may, by means of this formula, cal- 
culate the relative volume of the steam gene- 
rated under a given pressiune, as soon as we know 
the temperature answering to that pressure in 
steam at the maximum of density for its tem- 
perature. 

It is what we have done in the construction of 
the following Table. The second column has been 



OF THE MECHANICAL ACTION OF THE STEAM. 59 

formed by calculating the temperature of the steam 
at the maximum density, from the formulae which 
we have given in the first section of this chapter. 
Then using this series of temperatures in the for- 
mula which precedes, we have concluded the third 
column, or the relative volumes of the steam in 
contact with the liquid, under all the pressures 
comprised between 1 and 8 atmospheres. This 
Table will, in consequence, dispense with all cal- 
culation with regard either to the research of the 
temperatures, or to that of the relative volumes 
of the steam; and its extent will suffice for all 
applications that occur in the working of steam 
engines. 

When we speak of steam generated under a given 
pressure, we understand the steam considered at the 
moment of its generation, and consequently still 
in contact witli the liquid. We have explained 
elsewhere that the volume of the steam, compared 
to that of the water which has produced it, is 
precisely what we call the relative volume of the 
steam. 



60 



CHAPTER II. 



Table of the tenq^eraivre and volume of the steam gene- 
rated under different pressureSy compared to the volume 
of the water that has produced it. 



Total pres- 
sure, in 
English 

pounds per 

square 

inch. 


Corre- 
sponding 
tempera- 
ture, by 
Fahren- 
heit's ther- 
mometer. 


Relative vo- 
lume,or volume 
of the steam 
compared to 
the volume of 
the water that 
hasproducedit 


Total pres- 
sure, in 
English 

pounds per 

square 

inch. 


Corre- 
sponding 
tempera- 
ture, by 
Fahren- 
heit's ther- 
mometer. 


Relative vo- 
lume,orvolume 
of the steam 
compared to 
the volume of 
the water that 
hasproducedit. 


1 


102-9 


20954 


37 


263-7 


727 


2 


1261 


10907 


38 


265-3 


710 


3 


141-0 


7455 


39 


266-9 


693 


4 


152-3 


5695 


40 


268-4 


677 


5 


161-4 


4624 


41 


269-9 


662 


6 


169-2 


3901 


42 


271-4 


647 


7 


1760 


3380 


43 


272-9 


634 


8 


182-0 


2985 


44 


274-3 


620 


9 


187-4 


2676 


45 


275-7 


608 


10 


192*4 


2427 


46 


2771 


596 


11 


197-0 


2222 


47 


278-4 


584 


12 


201-3 


2050 


48 


279-7 


573 


13 


205-3 


1903 


49 


2810 


562 


14 


209-0 


1777 


50 


282-3 


552 


15 


2130 


1669 


51 


283-6 


542 


16 


216-4 


1572 


52 


284-8 


532 


17 


219-6 


1487 


53 


286-0 


523 


18 


222-6 


1410 


54 


287-2 


514 


19 


225-6 


1342 


55 


288-4 


506 


20 


228-3 


1280 


56 


289-6 


498 


21 


231-0 


1224 


57 


290-7 


490 


22 


233-6 


1172 


58 


291-9 


482 


23 


236-1 


1125 


59 


293-0 


474 


24 


238-4 


1082 


60 


294-1 


467 


25 


240-7 


1042 


61 


294 9 


460 


26 


243-0 


1005 


62 


295-9 


453 


27 


245-1 


971 


63 


2970 


447 


28 


247-2 


939 


64 


298-1 


440 


29 


249-2 


909 


65 


299-1 


434 


30 


251-2 


882 


66 


300-1 


428 


31 


253-1 


855 


67 


301*2 


422 


32 


255-0 


831 


68 


302-2 


417 


33 


256-8 


808 


69 


303-2 


411 


34 


258-6 


786 


70 


304-2 


406 


35 


260-3 


765 


71 


305-1 


401 


36 


2620 


746 


72 


306*1 


396 



OF THE MECHANICAL ACTION OF THE STEAM. 61 



Total pces- 
sure, in 
Sngliah 

pounds per 
aqnare 
inch. 


Corre- 
sponding 
tempera- 
tnre, by 
Fahren- 
heH's ther- 
mometer. 


Relative vo- 
lnme,or volume 
of the steam 
oompared to 
the volume of 
the water that 
has produced it. 


Total pres- 
sure, in 
En^ish 

pounds per 

square 

inch. 


Corre- 
sponding 
tempera- 
ture, by 
Fahren- 
heit's ther- 
mometer. 


Relative vo- 
lume,or volume 
of the steam 
compared to 
the volume of 
the water that 
has produced it. 


73 


307- 1 


391 


92 


323-5 


317 


74 


3080 


386 


93 


324-3 


313 


75 


308-9 


381 


94 


325-0 


310 


76 


309*9 


377 


95 


325-8 


307 


77 


310-8 


372 


96 


326-6 


305 


78 


311-7 


368 


97 


327-3 


302 


79 


312-6 


364 


98 


328-1 


299 


80 


313-5 


359 


99 


328-8 


296 


81 


314-3 


355 


100 


329-6 


293 


82 


315-2 


351 


105 


333*2 


281 


83 


316-1 


348 


120 


343-3 


249 


84 


316-9 


344 


135 


352-4 


224 


85 


317-8 


340 


150 


360-8 


203 


86 


318-6 


337 


165 


368*5 


187 


87 


319-4 


333 


180 


375-6 


173 


88 


320-3 


330 


195 


382-3 


161 


89 


321 1 


326 


210 


388*6 


150 


90 


321-9 


323 


225 


394-6 


141 


91 


322-7 


320 


240 


400-2 


133 



Sect. IV. Direct relation between the relative vo- 
lumes and the pressures^ in the steam in contact 
mth the li^id. 



It has just been seen, from the formulae given 
in the preceding section, that the density and 
the relative volume of the steam, whether separated 
from the liquid or not, are deduced from the know- 
ledge of the simultaneous pressure and temperature. 
It is likewise known that in the steam in contact 



62 CHAPTER II. 

with the liquid the temperature depends imme- 
diately on the pressure. It should therefore be 
possible to find a relation proper to determine 
directly the relative volume of the steam in con- 
tact with the liquid, or, in other words, of the 
steam at the maximum density and pressure for 
its temperature, by means of the sole knowledge 
of the pressure under which it is formed. 

The equation which gives the relative volume of 
the steam in any state whatever, in terms of its 
pressure and temperature, has been given above. 
We have also shown the formulae which serve to 
find the temperature in terms of the pressure, in 
steam in contact with the liquid. Eliminating 
then the temperature from the equation of the 
volumes and that of the temperatures, we shall 
obtain definitively the relation sought, or the rela- 
tive volume of the steam at the maximum density, 
in terms of the pressure only. 

But here starts the difficulty. First, M. Biot's 
formula not being soluble with reference to the 
temperature, does not admit the necessary elimina- 
tion. In the next place, the assemblage of the 
three formulae presented above, which are made to 
succeed each other, suit very well in the forma- 
tion of tables of correspondence between the pres- 
sures and the temperatures, when that is the end 
proposed. Likewise, in an inquiry relative to the 
expansion of the steam in an engine, when it is 
known precisely within what limits of pressure 



OF THB MECHANICAL ACTION OF THE STEAM. 63 

that expansion will take place, it may immediately 
be discerned which of the three formulae is ap- 
plicable to the case to be considered, and then t may 
be eliminated between that formula and the equation 
of volumes. But if the question regards, for in- 
stance, the case wherein the steam generated in 
the boiler under a pressure of 8 or 10 atmospheres 
might, according to the circumstances of the motion, 
expand during its action in the engine, either to a 
pressure less than 1 atmosphere, or to a pressure 
between 1 and 4 atmospheres, or, in fine, to a pres- 
sure superior to 4 atmospheres ; then we shall not 
know which of the three formulae to use in the 
elimination, and it will be impossible to arrive at 
a general equation representing the effect of the 
engine in all cases. 

Besides, were we even to adopt any one of those 
equations, the radicals they contain would render 
the calculation so complicated as to make it unfit 
for practical applications. 

The equations of temperature hitherto known 
cannot then solve the question that presents itself, 
that is to say, satisfy the wants of the calculation of 
steam engines in this respect; and, consequently, 
the only means left is to seek, in a direct manner, 
an approximate relation, proper to give immediately 
the relative volume of the steam at the maximum 
density in terms of the pressure alone. 

With this view M. Navier had proposed the 
expression : 



64 CHAPTER II. 

1000 



•09 + 0000484 p • 

in which fi is the relative volume, or the ratio of the 
volume of the steam to that occupied by the same 
weight of water, and p the pressure expressed in 
kilograms per square metre. 

It would be easy to transform this formula into 
English measures; but as it deviates considerably 
from experience for pressures below the atmosphere, 
and therefore was never intended to apply to con- 
densing engines; and as, moreover, for non-con- 
densing or high pressure engines, it is not nearly 
so exact as the formula which we are going to 
propose, we shall only present here the last one 
in English measures. 

Formula for high pressure engines : 

10000 

''"" 1-421 +0023p' 

In this expression fi represents the relative volume 
of the steam, and p is its pressure expressed in lbs. 
per square foot. 

To give a precise idea of the approximation given 
by this formula, we here subjoin a Table of the 
values it furnishes for the principal points of the 
scale of pressures. It will be remarked that in high 
pressure engines, the steam can hardly be spent at 
a total pressure less than two atmospheres, by 
reason of the atmospheric pressure, the friction of 
the engine, and the resistance of the load. Therefore 



OF THE MECHANICAL ACTION OF THE STEAM. 65 



it is needless to require of the formula exact vo- 
lumes for pressures less than two atmospheres. 

Relative volume of the steam generated under different 
pressures f calculated by the proposed formula. 









Volume calcula- 




Total pressure 

of the steam, in 

pounds per square 

inch. 


Volume of the 

steam, calculated 

by the ordinary 

formuhe. 


ted by the pro- 
posed formula for 
high-pressure 
non-condensing 
engines. 




15 


1669 


>> 




20 


1280 


1243 




25 


1042 


1031 




30 


882 


881 




35 


765 


768 




40 


677 


682 




45 


608 


613 




50 


552 


556 




55 


506 


509 




60 


467 


470 




65 


434 


436 




70 


406 


406 




75 


381 


381 




80 


359 


358 




85 


340 


338 




90 


323 


320 




105 


281 


276 




120 


249 


243 




135 


224 


217 




150 


203 


196 



Sbct. V. Of the constituent heat of the steam in 

contact with the liquid. 

There is yet an inquiry, relative to the properties 
of steam, which has long fixed the attention of 
natural philosophers : it is that of the quantity of 
heat necessary to constitute the steam in the state 

F 



66 CHAPTER II. 

of an elastic fluid under various degrees of elas- 
ticity. 

It is well known that when water is evaporated 
under the atmospheric pressure, in vam new quan- 
tities of heat may be added by means of the fur- 
nace ; neither the temperature of the water, nor that 
of the steam, ever rise above 100° of the centigrade 
thermometer, or 212° of Fahrenheit. All the heat 
then which is incessantly added to the liquid must 
pass into the steam, but must subsist there in a 
certain state which is called latent^ because the 
heat, though really transmitted by the fire, remains 
nevertheless without any efiect upon the thermo- 
meter, nor does it afterwards become perceptible 
till the moment of disengaging itself, on the steam 
being condensed. 

This latent heat evidently serves to maintain the 
molecules of water in the degree of separation suit- 
able to their new state of elastic fluid; and it is 
then absorbed by the steam, in a manner similar 
to that which is absorbed by the water, on passing 
from the solid state, or state of ice, to the Uquid. 
But it is important to know the quantity of the 
latent heat, in order to appreciate with accuracy 
the modifications the steam may undergo. 

Some essays made by Watt had already elicited 
that the steam, at the moment of its generation, 
or in contact with the liquid, contains the same 
quantity of total heat, at whatever degree of tension, 
or, in other words, at whatever degree of density, 



OF THE MECHANICAL ACTION OF THE STEAM. 67 

it may be formed. The experiments of Messrs. 
Sharpe and Clement have since confirmed this re- 
sult. From them is deduced, that the quantity 
of latent heat contained in the steam in contact 
with the liquid is less and less, in proportion as 
the temperature is higher; so that the total heat, 
or the sum of the latent heat plus the heat indicated 
by the thermometer, forms in sdl cases a constant 
quantity represented by 650° of the centigrade ther- 
mometer, or, 1 1 70° of Fahrenheit's. 

Southern, on the contrary, has concluded from 
some experiments on the pressure and temperature 
of steam, that it is the latent heat which is con- 
stant ; and that, to have the total quantity of heat 
actually contained in steam formed at a given tem- 
perature, that temperature must be augmented by 
a constant number, representing the latent heat 
absorbed by the steam in its change of state. 

Some authors have deemed this opinion more 
rational, but the observations we are about to 
relate seem to us to set the former beyond all 
doubt. 

It is known, that when an elastic fluid dilates 
itself into a larger space, the dilatation is invari- 
ably attended with a diminution of temperature. 
If, then, the former of the two laws be exact, it 
follows that the steam, once formed at a certain 
pressure, may be separated from the liquid, and 
provided it lose no portion of its primitive caloric, 



68 CHAPTER II. 

by any external agent, it may dilate into greater and 
greater space, passing at the same time to lower and 
lower temperatures, without ceasing on that account 
to remain at the maximum density for its actual 
temperature. In effect, since we suppose that the 
steam has in reality lost no portion of its total heat, 
the consequence is, that it always contains precisely 
as much as suffices to constitute it in the state of 
maximum density, as well at the new temperature 
as at the former. 

If, on the contrary, Southern's law be exact, 
when the steam, once separated from the liquid, 
will diminish in «[ensity as it dilates into a larger 
space, it will not remain at the maximum density 
for the new temperature. To admit indeed that it 
would do ^o, would be to verify Watt's law, since 
the new steam would be at the maximum density, 
although containing precisely the same quantity 
of total heat as the old. But since we admit, on 
the contrary, that the primitive steam contained 
more heat than was necessary to constitute the new 
at the maximum density, it follows that the surplus 
heat, now liberated, will diffuse itself in the new 
steam; and as this is separated from the liquid, 
the increase of heat cannot have the effect of in- 
creasing the density of the steam, but will be alto- 
gether sensible in the temperature. Thus the 
result will be, a steam at a certain density, indi- 
cated by the spaces into which it is dilated, and 



OF THB MECHANICAL ACTION OF THE STEAM. 69 

at a temperature higher than what is suitable to 
that density, in steams at the maximum of density 
for their temperature. 

Now, in a numerous series of experiments, of 
which we shall speak hereafter, we have found 
that in an engine whose steam-pipes were com- 
pletely protected against all external refrigeration, 
the steam was generated at a very high pressure 
in the boiler; and, after having terminated its 
action in the engine, escaped into the atmosphere 
at pressures very low and very varied ; and that in 
every case the steam issued forth precisely in the 
state of steam at the maximum of density for its 
temperature. Southern's law then is inadmissible, 
unless any one choose to suppose that in these 
varied changes of pressure the steam lost, by 
contact with the very same external surfaces, al- 
ways precisely and strictly just that quantity of 
heat, sometimes very considerable, at other times 
very small, by which its temperature should have 
increased. Consequently the law of Watt is the 
only one supported by the facts. 

The total quantity of heat contained in the steam 
in contact with the liquid, and under any pressure 
whatever, is then a constant quantity ; and accord- 
ing as the sensible heat increases, the latent heat 
diminishes in an equal quantity. 

On the other hand, according to the same law, 
if we conceive water to be enclosed in a vessel 
capable of sufficient resistance, and submitted to 



70 



CHAPTER 11. 



temperatures of greater and greater intensity; the 
latent heat of the steam thence arising will be less 
and less as the sensible heat or temperature shall 
become greater ; and as soon as the steam shall be 
generated at a temperature equal to 650® centigrade 
or 1170° of Fahrenheit, it will cease to absorb 
heat in a latent state, and will no longer receive 
any portion of it, but which will be sensible on 
the thermometer. We must then conclude that 
at this point the steam will have a density equal 
to that of water ; since in passing from one state 
to another, it requires no farther increase of caloric, 
as would be necessary if any farther increase of se- 
verance were to take place between the molecules. 
Thus the water, though still contained in the vessel, 
will all have passed into the state of steam, so that 
there will be no more steam in contact with the 
liquid. From this moment, then, new quantities of 
heat may be applied to the vessel ; but instead of 
acting on a liquid, which passes to the state of gas, 
by absorbing latent heat, it will now only act on an 
elastic fluid, and therefore all the increase of heat 
will, as in all gases, become sensible on the ther- 
mometer. 

This observation explains the difficulty which 
would otherwise present itself; viz., that beyond 
650° centigrade or 1170° of Fahrenheit, the pre- 
ceding law could not subsist without the latent 
heat becoming a negative quantity, which is im- 
possible. 



OF THB MECHANICAL ACTION OF THE STEAM. 7l 

Sect. VI. — Of the conservation of the maximum 
density of the steam for its temperature ^ during its 
action in the engine. 

When an engine is at work, the steam is gene- 
rated in the boiler at a certain^ pressure ; from 
thence it passes into the cylinder, assuming a dif- 
ferent pressure, and then, if it be an expansive 
engine, the steam, after its separation from that of 
the boiler, continues to dilate itself more and more 
in the cylinder, till the end of the stroke of the 
piston. It is commonly supposed that, during all 
the changes of pressure which the steam may un- 
dergo, its temperature remains the same, and the 
consequent conclusion is that, during the action of 
the steam in the engine, its density or relative vo- 
lume follows the law of Boyle or Mariotte ; that is 
to say, the relative volume varies in the inverse 
ratio of the pressure. This supposition simplifies 
indeed the formulae considerably, but we shall pre- 
sently see that it is contrary to experience ; and 
therefore it becomes necessary to seek what is the 
true law, according to which the steam changes 
temperature in the engine, at the same time that its 
pressure changes. And as calculations relative to 
the effects of steam depend essentially on the 
volume it occupies, we must seek also what changes 
that volume undergoes, by reason of the variations 
of temperature and pressure which take place in 
the steam during its action. 



72 CHAPTER II. 

We shall then substitute for the relation pre- 
cedently indicated, according to Mariotte's law, 
another more real, and, what is essentially necessary 
to calculate the effects of steam with accuracy, 
deduced from the facts themselves. 

We have just^ said that the calculations relative 
to steam engines suppose the steam to preserve 
invariably its original temperature, which allows 
the application of Boyle's or Mariotte's law to 
all the changes of density or of pressure it may 
undergo. However, as it is known that elastic 
fluids never dilate without cooling in some degree, 
this supposition obviously could not be realized, but 
on condition that the steam have time to recover 
from the bodies with which it is in contact, sup- 
posed to be* sufficiently heated, the quantity of 
caloric necessary to restore its temperature, after 
expansion, to the same degree at which it was 
before. Now, the rapidity of the motion of the 
steam in the cylinders and the pipes, and the 
natural temperature of those pipes, which makes 
them rather liable to take caloric from the steam 
than to supply it with caloric, will not suffer the 
admission of such an hypothesis. 

To obtain satisfaction on this head, in a numerous 
series of experiments, we adapted to the boiler of a 
locomotive engine a thermometer and an air-gauge 
or manometer ; we appUed also two similar instru- 
ments to the pipe through which the steam, after 
having terminated its action in the engine, escaped 



OF THE MECHANICAL ACTION OF THE STEAM. 73 

into the atmosphere ; and we observed their simul- 
taneous indications. The steam was generated in 
the boiler at a total pressure varying from 40fl>s. to 
65fts. per square inch, and escaped into the atmo- 
sphere at a pressure varying, according to different 
circumstances, from 20fts. to 15fl>s. per square 
inch. Had the steam preserved its temperature 
during its action in the engine, it would have issued 
forth with the pressure, for instance, of 1 5 fl>s. per 
square inch, but with the temperature proper to the 
pressure at which it had been formed, that is, 65fts. 
per square inch. Now, nothing Uke this took place : 
during some hundreds of experiments wherein we 
observed and registered these effects, we found in- 
variably that the steam escaped precisely with the 
temperature suitable to its actual pressure. 

In effect, the divisions of the thermometer em- 
ployed indicated the pressure in steam in contact 
with the Uquid ; that is to say, the degrees of 
temperature having been first marked in the ordi- 
nary way, the temperatures had been afterwards 
replaced, from known Tables, by the corresponding 
pressures in steam at the maximum of pressure or 
of density for its temperature. This instrument 

m 

showed then at every moment the maximum pres- 
sure corresponding to the actual temperature of the 
steam. On the other hand, the air-gauge measured 
directly the real pressure of the steam. The two 
instruments then could agree only so long as the 
real pressure of the steam was at the same time the 



74 CHAPTER II. 

maximum pressure corresponding to the tempe- 
rature of that steam. But, during the whole course 
of the experiments, the thermometer was found to 
give identically the same degree of pressure as the 
air*gauge, and it equally agreed with a siphon- 
manometer which we had superadded to the appa- 
ratus at the point of the outlet of the steam. The 
steam then was generated in the boiler at a certain 
very high pressure, and quitted the engine at a 
very low one ; but, on its leaving the engine, as 
well as at the moment of its production, that steam 
was at the maximum of pressure or of density for 
its temperature, that is to say, it was precisely in 
the same state in which it would have been, had it 
risen immediately from the liquid at its actual 
pressure. 

We will not relate all the experiments in which 
we have observed this result, since it would be a 
mere repetition of the same thing, and since, in 
order at the same time to attain other determi- 
nations relative to the engine, and particularly that 
of the pressure due to the blast-pipe, as will here- 
after appear, we necessarily made a very great 
number of observations on the subject ; but to give 
an idea at least of the results, we will present a 
few series of them in the following Table : 



OF THE MBCHAXICAL ACTION OF THE STEAM 



#D 



EjrperimemiB am the changes of pressure and ten^prrature 
of the steamk, Atring its action in the engine. 



Total prescareof 

the suaiBv in ft*^ 

: per iq. iBch, txt 

thff ■KHDCBl of( 

its gcjitiaiioB in 
thehoilrr^bTtbe 
air-fuige aiid by 
tlie thenDometer. . 


1 

1 


• 

1 
Toul pressaiv of tb« 
fteam, in lbs. per sq. , 
incb, at the moment oi ', 


I 

CormpoBding 

temperature, in 

decrees o€ 

Fahn^nheit*s 

thermonieter. 


tnnpcnture, | 

Fahrenheit'i 
thomoiDCier. 


its leaving the cmpmt, 

by the jbr the tber- 
air-fange. momcter. ■ 


59 


293 


16-5 


16-5 1 


218 


GO 


2941 


16-5 


16 5 


218 


61 


294-9 


16-5 


16-5 


218 


63 


297 


16-5 


16-5 


218 


62 


295-9 


17-5 


17-5 


2211 


61 


294-9 


18-5 


185 


2241 


61 


294-9 


19-5 


19-5 


226 9 


59 


293 


19-5 


19-5 


226-9 


59 


293 


20-25 


20-25 


229 


59 


293 


20-5 


20-5 


229-6 


59 


293 


20-25 


20-25 


229 


46 


2771 


18 


18 


222-6 


49 


281 


18-5 


18-5 


224-1 


54 


287-2 


20 


20 


228-3 


56 


289-6 


21 


21 


231 


51 


283-6 


21-5 


21-5 


282-3 


51 


283-6 


21-25 


21-25 


231-6 


53 


286 


20-5 


20-5 


229-6 


52 


284-8 


19 


19 


225-6 


51 


283-6 


19 


19 


225-6 


52 


284-8 


19 


19 


225-6 


51 


283-6 


19 


19 


225-6 


1 51 


283-6 


18-5 


18-5 


224- 1 


53 


286 


18-5 


18-5 


224- 1 


54 


287-2 


18-5 


18-5 


224- 1 


57 


290-7 


18-5 


18-5 


224- 1 


58 


291-9 


18-5 


18-5 


2241 


62 


295-9 


17-25 


17-25 


220-3 


64 


2981 


17-75 


17-75 


221-8 


62 


295-9 


18 


18 


222-6 


61 


294-9 


18-75 


18-75 


224-8 


64 


298-1 


21-5 


21-6 


232*3 


60 


294- 1 


^1-5 


21-5 


232*3 


60 


294- 1 


20-75 


20-75 


230-3 


61 


294-9 


20-75 


20-75 


230-3 


62 


295-9 


21-25 


21-25 


231-6 


63 


297 


21-75 


21-75 


232*9 



76 CHAPTER II. 

We see from these experiments, that the steam, 
after having been generated in the boiler at a very 
high pressure and temperature, lowered its pressure 
more or less in the engine, but that its temperature 
lowered at the same time, and in such sort that the 
steam was always at the maximum of pressure or of 
density for its temperature. 

In the engine submitted to experiment, the 
steam, throughout its action, was completely pro- 
tected against all external refrigeration; for the 
pipe which conducted it from the boiler to the 
cylinder was immerged into the steam of the boiler 
itself, as far as the point where it entered the 
smoke-box. Then, as well in the interval which 
separates that point from the entrance of the cy- 
linder as during its action in the cylinder itself, and 
from its quitting the cylinder to the orifice of the 
blast-pipe, the steam was continually traversing 
passages entirely enclosed in the smoke-box, and 
consequently in immediate contact with the flame 
and hot air proceeding from the furnace. The steam 
could not then be liable to any external refrigera- 
tion. 

The above-mentioned experiments referred then 
to an engine perfectly guarded against any external 
refrigeration. On the other hand, supposing an 
engine wherein these external causes of refrigeration 
were not provided against, the effect will be first to 
operate the condensation of a part of the steam 
produced, and there will consequently exist in the 



OF THE MECHANICAL ACTION OF THE STEAM. 77 

passages traversed by the steam a certain quantity 
of ¥rater in its liquid state. It will be precisely the 
same in the cylinder of a condensing engine, after 
the imperfect condensation of the steam. In each 
of these two cases, the remaining steam will be 
found materially in presence of the liquid, and 
consequently will again be necessarily at the maxi- 
mum of density for its temperature. 

Finally, a third case might be supposed, that in 
which the steam should, on the contrary, acquire 
heat after its separation from the water of the 
boiler. Then, contrary to what has been seen to 
take place in the locomotive engine mentioned 
above, it is plain that the steam would acquire a 
temperature above that which is proper to steam at 
the maximum density for its temperature ; but this 
case does not occur in steam engines, and it will 
therefore be useless to dwell on it. 

It is consequently to be concluded from the fore- 
gping, that in steam engines more or less perfectly 
guarded against all external refrigeration, the steam 
remains always, during its action in the engine, in 
the state of maximum density for its temperature, 
as if it had never ceased to be in contact with the 
generative liquid. 

Now, we have shown in the fourth section of this 
chapter, that, with regard to steam in contact with 
the liquid, the relative volume may be expressed in 
terms of the pressure by a very simple formula, 
which we may present generally under the form 



78 CHAPTER II. 

n+qp 

This analogy, in which n and q will have the nume- 
rical values already indicated, will then be applicable 
to all the changes of volume of the steam during its 
action in the engine. 

From this equation, if we suppose that a certain 
volume of water, represented by S, be transformed 
into steam at the pressure p, and that we call M the 
absolute volume of steam which will be produced by 
it, we shall have 



S «+?p 

If afterwards the same volume of water be trans- 
formed into steam at the pressure p\ and that we 
call M' the absolute volume of the resulting steam, 
we shall have also 

M' 1 

S n+jp' 

Consequently, between the absolute volumes of 
steam which correspond to the same weight of 
water, we shall have the definitive relation, 

M n , 
-+P 
9 

that is to say : the volumes of the steam will be, 

not in the inverse ratio of the pressures, as was 

supposed in admitting Boyle's or Mariotte's law, 



OF THE MECHANICAL ACTION OF THE STEAM. 79 

but in the inverse ratio of the pressures augmented 
by a constant quantity. 

From the equation (6) is likewise drawn the 
analogy 

And the two equations (6) and (c) will serve to 
determine, either M, or p^ accoi^ing to the one of 
these two quantities, which will be unknown. 

As, in all calculations relative to the effects of 
steam engines, the volume occupied by a given 
weight of steam forms the important element of the 
calculation, it is very obvious that the use of the 
principle of the conservation of the maximum density 
of the steam for its temperature ^ during its action in 
the engine, and the formulae by which we have 
represented it, will tend to the avoiding of many 
considerable errors in the results. 

If we consider a condensing engine in which the 
steam generated at the pressure of 8 atmospheres, 
or 120 fts. per square inch, shall expand to lOfts. 
per square inch ; then, in the usual mode of calcula- 
tion, it will be supposed that the steam, diuing its 
expansion, will preserve its temperature, and that 
its volume will vary in the inverse ratio of the 
pressures. The volume of the steam at the pres- 
sure of 120 lbs. per square inch is 249 times that of 
the water which produced it. If its temperature 
remained unchanged during its action in the engine, 
its volume after the expansion would become 



80 CHAPTER II. 

249 X ^ =2988. 

The supposition, then, amounts to admitting that 
under the pressure of 10 lbs. per square inch, the 
volume of the steam would be 2988 times that of 
the water. Now, from accurate Tables, this volume 
is 2427. An error, then, is induced of ^ on the real 
volume of the steam, that is to say, on the effect of 
the engine ; and this error will be almost entirely 
avoided by the use of our formula suitable to con- 
densing engines {Theory of the Steam Engine^ chap. 
II. sect, iv.), since it gives in this case 2417, in- 
stead of 2427, that is to say, it differs inconsiderably 
from the true volume of the steam. 

In non-condensing engines, the error which re- 
sults from the application of Mariotte's law is again 
very sensible, though less considerable than in the 
preceding engines. If, in fact, we suppose an engine 
wherein the steam be generated at the pressure of 
5 atmospheres, or 75Ibs. per square inch, and ex- 
pended at the pressure of 30fts. per square mch, or 
about 2 atmospheres, as the volume of the steam 
formed under the pressure of 75 lbs. per square inch 
is 381 times the volume of the water, it is plain 
that, if the action of the steam took place without 
the temperature changing, its volume, at the moment 
of its action, would be represented by the number 

381 X 1=952. 
But from exact Tables, the volume of the steam 
formed at the pressure of 30fts. per square inch is 



OF THE MECHANICAL ACTION OF THE STEAM. 81 

really 882 times the volume of the water. Ad- 
mitting, by the fact, the former number instead of 
the latter, an error will be committed of about ^ on 
the real volume of the steam, and consequently on 
the effect of the engine ; and that error will be 
totally avoided by using the Tables which we have 
given of the volume of the steam. Using our 
formulae for non-condensing engines, the resulting 
number for the volume of the steam will be 881 
instead of 882. In this case also will thus be 
avoided the above-mentioned error. 

We must however add, that with respect to slight 
differences of pressure, such as occur in a great 
number of cases, the error resulting from the use of 
Mariotte's law may become quite unnoticeable. 



Q 



CHAPTER III. 

OF THE PRESSURE OF THE STEAM. IN LOCOMOTIVE 

ENGINES. 



ARTICLE I. 

OF THE SAFETY-VALVES. 

Sect. I. Of the Pressure calculated according to the 
Levers and the Spring -balance. 

When an elastic fluid is confined in a closed 
vessel, it produces in every direction, on the sides 
of the vessel, a pressure, which is the result of its 
elastic force, and which gives the exact measure of 
that force. If, the vessel being already filled with 
steam, a fresh quantity is continually added, the 
elastic force of the steam will augment more and 
more, and consequently also the pressure it produces 
on every square inch of the surface of the vessel. 
Now if at one point of the vessel there be a valve, 
that is to say, an aperture, closed with a moveable 
piece supporting a certain weight, it is clear that, as 
soon as the steam contained in the vessel produces 
upon the moveable plate a pressure equal to that 
of the weight which holds it down in the opposite 



OF THE PRESSURE. 83 

direction, the plate will begin to be lifted up ; the 
passage will then be opened, and the steam escaping 
through the aperture, will show that its pressure was 
greater than the weight that loaded the plate or 
valve. 

It must however be observed, that the resistance 
which opposes the egress of the steam does not 
consist only in the weight that has been placed on 
the valve. Besides that weight, the atmosphere 
produces also on the valve a certain pressure, as 
well as upon every other body with which it comes 
in contact. That pressure is known to be equal 
to 14"7ibs. per square inch. It is therefore the 
weight, added to the pressure of the atmosphere, 
that gives the real measure of the elastic force of 
the steam ; while the weight alone represents only 
the surplus of the pressure over the atmospheric 
pressure, or what is called the effective pressure of 
the steam. Consequently, when a valve has a sur- 
face of five square inches, and supports a weight of 
250fl>s., which, divided between the five square 
inches, gives a resistance of 50 lbs. per inch, that 
amoimt of 50 fl>s. expresses the effective pressure of 
the steam, a valuation frequently made use of on 
account of its convenience for calculation, whereas 
64*7 fl>8. is the real resistance opposed, and therefore 
the real pressure of the steam. 

On this principle are grounded the means of 
measuring the pressure in steam engines, but in- 
stead of imposing directly a weight on the valve. 



84 CHAPTER III. 

which weight must needs be considerable, a lever is 
used; and as moreover a heavy body suspended 
at the extremity of such lever would be liable to 
continual jerking, during the motion of the en- 
gine, which would cause an incessant opening and 
shutting of the valve, this weight is replaced by an 
equivalent spring. 

Figure 1 6 represents the apparatus used in loco- 
motive engines. The point C is a fixed pivot round 
which the lever CB may move up and down. At 
the point A this lever presses on the valve S by 
means of a pin, and is held at its extremity B by 
the above-mentioned spring. This consists of a 
spiral, which by being more or less compressed, is 
able to support in equilibrium, and consequently to 
represent, larger or smaller weights. In other words, 
it is a spring-balance, such as is used for weighing 
in daily occurrences. 

This balance consists of a rod T (fig. 16) which 
is held in the hand, and to which is fastened a plate 
with a narrow oblong aperture in it. Behind this 
plate, and in a cylindrical tube, is a spring, the foot 
of which rests on the basis L, which is fixed to the 
plate. At its other end, this same spring is pressed 
by a moveable transverse bar mn. At the inferior part 
of the apparatus is a rod P, to which are fastened the 
objects that are to be weighed. The prolongation of 
the bar mn projects through the aperture of the plate, 
and is terminated by an index which appears on the 
outside, and which slides up and down the aperture in 



OF THB PRESSURE. 85 

proportion as the spring is more or less compressed. 
Divisions are engraved along that same aperture. In 
order to mark them, known weights of lib., 2 lbs., 
&e. are successively suspended at P, and according as 
those weights, by pressing on the sprmg, cause the 
index to rise, the corresponding divisions are marked. 
The consequence of this is, that when an object 
of unknown weight is suspended at P, and makes 
the index rise to the point marked 10, that is to 
say, to the same point to which a known weight of 
lOfts. made it rise, we conclude that the object also 
weighs lOfts. This is the sort of balance which is 
used for measuring the pressure in locomotive en- 
gines. We see that, by taking it off from the engine, 
and suspending known weights to it, the divisions 
may easily be verified, after the balance is graduated. 
On the engine, the foot P of the balance, where 
the object to be weighed would be suspended, is 
fixed in a solid manner to the boiler ; and the rod 
T, which would be held in the hand in common 
weighing, is fastened to the end of the lever. This 
rod passes through an aperture cut through the end 
of the lever, and is fixed above it by a screw which 
rests upon the lever. When it is required that this 
balance shall produce a pressure of 10 lbs., nothing 
more is necessary than to lower the screw until the 
spring rises to the point marking 10 lbs., and the 
same for any other weight. 

Vice versd^ the steam being in the boiler at an 
unknown degree of pressure, if we loosen gradually 



86 CHAPTER III. 

the screw until the steam begins to raise the valve, 
that is to say, until its pressure stands in equilibrio 
with the pressure of the spring, the pressure of the 
steam will be known, for the degree then marked 
by the index will show the weight which is equal 
to it. 

Kiiowing the weight marked on the balance, or 
represented by the tension of the spring, it is easy 
to deduce the resulting pressure on the valve per 
unit of surface ; for the weight multiplied by the pro- 
portion of the two arms of the lever gives, firstly, 
the total pressure on the whole valve, and this di- 
vided by the area of the valve gives the pressure 
acting on each unit of its surface. Thus P being 
the weight inscribed on the balance, its effect on the 
point A will be 

BC 



PX 



AC 



and if the area of the valve be expressed by a, the 
pressure on the unit of surface will be 

^AC 

p = — 



a 



To avoid all necessity of calculation in this respect, 
the lever is often so constructed that the ratio of its 
two parts is expressed by the number itself which 
expresses the surface of the valve. That is, if the 
area of the valve is 5 square inches, the levers will 
be made in the proportion of 5 to 1 ; then the pres- 



OF THK PRESSURE. 87 

sure per unit of snriaoe of the valve is immediately 
given by the weight inscribed on the balance. 

If, for instance, we suppose a valve of 2^ inches 
in diameter, which makes very nearly 5 square 
inches of sur£aux, and that the two levers BC and 
AC be 15 inches and 3 inches, a weight of 50fts. 
marked on the balance will, from the ratio of the 
levers, act on the valve with a pressure of 5 times 
50^8., or 250 fts., which, divided among the 5 
square inches of surfece of the valve, will give 
50 fts. per square inch, which is precisely the weight 
marked on the balance. 



Sect. II. Of the corrections to be made to the weight 

marked by the Spring -balance. 

The calculation explained above gives the pressure 
acting on the valve. However, it will easily be con- 
ceived, by the manner in which the spring-balance 
acts upon the valve, that, to know the pressure 
which really opposes the egress of the steam, it is 
not sufficient to read the degree where the index 
stops, and to calculate the effect produced at the end 
of the lever, as we have done above. In fact, first, 
besides the weight represented by the spring, and 
which would be suspended at the end of the lever, it 
is clear that the weight of the lever itself causes a 
certain degree of pressure ; for before the steam is 
able to act on the spring, it must raise the whole 
weight of the lever. The same takes place in regard 



I 



88 CHAPTER III. 

to the disk of the valve, which must be raised before 
the steam can have anv action on the balance. — 
2. When any object is weighed with the hand, that 
object is suspended at the lower part of the balance, 
but then the hand supports the upper part, that is to 
say, the rod, with the spring to which it is fastened; 
and that effort is not taken into account, because 
it does not make a part of the weight. Here, on 
the contrary, the rod, the screw, and the spring, are 
an additional weight really suspended at the end of 
the lever, over and above the pressure marked by 
the spring ; they must all be raised before the spring 
can be pressed upon in any way, and can register 
any effort; they must therefore be taken into ac- 
count. The true pressure which takes place on the 
valve will consequently not be known, until are 
added to the weight marked in the balance : 1 . The 
pressure produced by the weight of the lever at the 
place of the valve ; 2. The pressure produced at the 
end of the lever by the weight of the rod and spring 
of the balance. 

To measure at once these two additional resist- 
ances, the following means may be used. First 
loosen completely the screw of the balance, till the 
spring no longer pulls on the lever, and till the valve 
bears no other weight than that of the lever itself, 
and its dependent apparatus. Then pass a string 
round the pivot A which rests on the valve, and 
having attached the extremities of this string to 
another spring-balance, raise the whole with the 



OF THE PRESSURE. 89 

hand, by means of this second balance, till you see 
the index of the balance of the engine stop at zero 
of weight. The additional weight sought will be 
indicated on the balance borne in the hand. It is in 
fact clear that, by this proceeding, all the additional 
weight on the valve is held in equiUbrio, and that if 
the valve could be maintained in this state while at 
work, every pound of pressure in the boiler would 
immediately mark one pound of pressure on the 
balance, since there would no longer be any addi- 
tional weight to raise. 

By this means, then, may be known the addition 
that ought to be made to the pressure indicated by 
the balance. It is found that, when the levers are 
36 inches in total length, of a usual thickness and 
with the balance commonly adapted to them, they 
produce on the valves an additional pressure of 7 to 
8 lbs. per square inch, and when they are 15 inches 
in total length with their corresponding apparatus, 
the additional pressure still amounts to 3 or 4 lbs. 
per square inch. This therefore is obviously a cor- 
rection not to be neglected, if in the calculation a 
certain degree of accuracy be required. 

Finally, there is another cause of error which it is 
proper to note here. 

In order that the valves may exs^^ctly close the 
opening to which they are applied, without being 
subject to contract an adhesion with the seat that 
supports them, it is necessary to make them slightly 
conical, or at least with a slanting border, as repre- 



90 CHAPTER III. 

sented in figs. 20 and 22. When these valves rest 
upon and completely fill their seat, it is very clear 
that the steam can only act upon their inferior sur- 
face; consequently, the area which we have ex- 
pressed ahove by a, must be taken after the inferior 
diameter of the valve. To be perfectly exact, this 
area ought even to be taken from the diameter of the 
orifice covered by the valve, for the latter might be 
constructed in the form of fig. 2 1 , where it is seen 
that the surface according to which the pressure is 
to be divided, is not ah but cd. Taking then the 
proper measurements, and calculating as we have 
done above, the exact pressure will be found for 
every case in which the valve rested upon the seat, 
or, if raised, was raised only for an instant, and 
in a very small degree ; but whenever the steam, 
being generated in greater quantity than it is ex- 
pended by the cylinders, escapes with force through 
the valve, it raises considerably the disk of the 
valve: the consequence then is, that, instead of 
acting merely on the inferior surface of the valve, 
it evidently acts on a greater surface, and which 
is still greater the more the valve is raised. 

The efiect of this alteration in the diameter of 
the valve, which at first sight appears triflmg, is 
in fact very considerable. Let us suppose, for in- 
stance, that we have a valve of 2*50 inches in dia- 
meter at the bottom, and 3 inches at the top. Let 
us further suppose that, by the efiect of the blowing 
of the steam, the valve has been raised so as to 



OF THE PRESSURE. 91 

have increased its real diameter onlv bv one-ei^rhth 
of an inch ; the surface of the valve, which was at 
first 

4 '91 square inches, 
has become 

5"41 square inches. 

Consequently, if we supjxjse the total weight sup- 
ported by the valve to be 245 lbs., that weight, 
when the valve is shut, will represent a pressure 
per square inch of 

245 

and when the valve is raised, that same weight will 
only represent a pressure of 

245 

3:^ = 45-27 lbs. 

The above established calculation, then, is to be 
depended on only, when the balance-screw can be 
lowered so as precisely to equilibrate the interior 
pressure, as has been said above, without, however, 
allowring the valve to rise. But the thing is not 
possible when the engine produces a surplus of 
steam beyond what its cylinders can expend, be- 
cause this steam must necessarily have an issue. 
In this case, then, the pressure is to be found only 
by recurring afterwards to the barometer-gauge, as 
we shall presently indicate. 



92 CHAPTER III. 



ARTICLE II. 

OP THE INSTRUMENTS SPECIALLY DESTINED TO 
MEASURE THE PRESSURE. 

Sect. I. Of the Barometer-gauge ^ or Syphon- 

manometer. 

The calculiitions just proposed can only be es- 
tablished by measuring and weighing divers parts 
of the engine, which requires time and care, and 
can be effected only when the machine has ceased 
working. The great utility then is obvious of an 
instrument which, at once and by the mere inspec- 
tion, shall give the exact measure of the pressure of 
the steam. With the aid of such an instrument, no 
case, not even that of the raised valve, opposes the 
smallest difficulty, nor needs any calculation. 

Several instruments have been imagined for this 
purpose. The syphon-manometer, which we shall 
notice first, is represented in fig. 18. This instru- 
ment is not portative, for which reason those we 
shall describe in the following sections, and which, 
moreover, are much less expensive, will of course 
be preferred to it for the use of locomotives. How- 
ever, as the manometer is the most accurate for 
the engine at rest, and as it may also serve for 
the graduation and verification of the others, its 
construction shall be shown here. 

The instrument is established on the same prin- 



OF THE PRESSURE. 93 

ciple as the common barometer. Mbm is a tube 
containing mercury, which ought not to rise above 
the two points M and m. FG is a water reservoir, 
the use of which is to keep the branch Mb con- 
stantly full of water, in proportion as the mercury 
descends in that branch. Its diameter is purposely 
much greater than that of the tube, in order that 
the upper level of the reservoir be not sensibly 
lowered by reason of the water which « it supplies to 
the tube. That level ought not to rise above the 
cock E, the use of which is to get rid of the surplus 
of water that may have been produced by condensa- 
tion on some former experiment. R is an opening 
closed by a cock, and through which mercury or 
water may, when wanted, be introduced into the 
instrument. Lastly, C is a tap on which a tube 
is screwed, the other end of which reaches the 
boiler of the engine. This tube is flexible, and 
usually made of tin ; it forms the commimication of 
the mercurial-gauge with the engine. At the point 
where it reaches the engine, it is screwed on a tap 
fixed to the boiler, and kept close by a cock. 

To prepare the instrument for use, an additional 
quantity of mercury is poured into it by the aperture 
R, in order to be sure that the instrument contains 
mercury at least to the height Mm. After this, the 
screw-bolt M is unscrewed, so that if there happen 
to be too much mercury it may run off. When 
this is done the screw-bolt is replaced, and an addi- 
tional quantity of water is also poured through R 



94 CHAPTER III, 

into the reservoir FG, and, should there be too 
much, it is also allowed to run off through the cock 
E. Then the instrument is put in communication 
with the boiler. The steam, arriving through the 
tube C in the upper part of the reservoir FG, presses 
on the water by virtue of its elastic force ; it con- 
sequently presses the mercury down in the branch 
M&, and makes it rise in the branch mb which is 
open at the top, until the weight of the mercury, 
thus raised, is equal to the pressure of the steam 
issuing from the boiler. A metal float borne on 
the surface of the mercury, at the point m, rises 
in proportion as that surface rises in the tube; 
and an index suspended to a thread which passes 
over a communication-pulley p, falls between the 
two tubes as the mercury rises in the branch bm^ 
and shows upon a graduated scale the variations 
that occur in the level of the mercury in the dif- 
ferent experiments. Supposing the length of the 
instrument from M to 6 be 6^ feet, or 78 inches, 
the ascending column may, if necessary, contain 
1 56 inches of mercury ; and as a column of 1 56 
inches of mercury with a basis of 1 square inch 
weighs about 80 lbs., such a column may serve to 
measure an effective pressure amounting to 809>8. 
per square inch. 

To graduate the scale of the instrument, we may 
begin by marking first the point zero. For this, 
the mercury and the water being poured in, as said 
above, the two branches must be left to communi- 



OF THE PRESSURE. 95 

cate freely with the atmosphere, and the point 
where the index stops will be the point sought, for 
that is the position which the float naturally takes 
when the branch Mb bears no more than the atmo- 
spheric pressure. 

The other extreme point of the scale must after- 
wards be marked. Let ir be the pressure we want 
to equilibrate; supposing the equilibrium established, 
let X be the height at which, by virtue of that same 
pressure tt, the mercury will stand above its natural 
level in the branch m. The mercury having risen 
in the branch m to the height x, it must have fallen 
by an equal quantity in the other branch ; for the 
mercury added on the one side can only proceed 
from what has been taken off on the other. The 
mercury in the branch M will therefore at the same 
time be at the point /, and the whole part of that 
branch, from the point x' to the point M, will be 
filled by the water from the reservoir. If through 
the point x' we draw an horizontal plane, the mer- 
cury which is under that plane will equilibrate itself 
in the two branches ; we have therefore nothing to 
do with it, and need only consider the conditions of 
equiUbrium for those parts which are above the 
plane in the two branches. Now, we have on the 
one side the pressure w, plus the weight of a column 
of water in height Ma7'= 07; and on the other side, 
we have a column of mercury in height 2x, plus the 
weight of the atmosphere. P being the weight of 
the column of mercury, F that of the column of 



96 CHAPTER III. 

water, and p that of the atmosphere, we shall have, 
smce there is an equilibrium, 

(w— p), which is the surplus of the real pressure of 
the steam over the atmospheric pressure, is called 
the effective pressure; and in all high-pressure 
steam engines it is this which is to be considered. 
The column of mercury, the weight of which we 
have expressed by P, having for its basis the basis 
of the tube which we shall express by 6, and for its 
height the height^ 2a:, its volume will be 2bx; S 
representing the density of the mercury, 2Sbx will 
be the mass of the same column ; and g expressing 
the accelerating force of gravitation, 2gSbx will be 
its weight : that is to say, we shall have 

P = 2gSbx. 

By the same reason, S" being the density of the 
water, the weight F of the column of water will be 
expressed by gS^bx, its basis being also 6, and its 
height Mx'=x. But the density of the water being 
expressed by 1 , that of the mercury is expressed by 
13- 568 ; thus we have 

^'^ 13^568' 
and consequently 

^ ~ 13-568 

On the other side, the effective pressure (w— p), 
in whatever manner it be expressed, may be replaced 



OF THE PRESSURE. 97 

by the weight of a column of mercury, that would 
produce the same pressure on the basis b. If then 
h be the height of that column, which it is easy to 
calculate, we shall have 

ir '^ p=^ gSbh ; 

and the equation of equilibrium will thus be 



gSbx 
2gSbx = jg.ggg +gcbh, 



which gives 



13-568 
a? = A X 26l36 ~ AxO-51913. 

The height A of a column of mercury, which may 
represent a given pressure, is easily found ; for we 
know that a column of mercury, one inch high, 
presses on its basis at the rate of 0*4948 lb. per 
square inch. The height of any other column may 
thus be proportionably calculated. Wishing, for 
instance, to represent a pressure of 70 lbs., we have 

70 in. 

h= 0:4043 X 1 = 141-47 inches; 

so that, by this value of A, the quantity sought x 
will be 

X = 141 -47 in. X 0-51913 = 7344 in. ; 

that is to say, that to correspond to an effective 
pressure of 70 lbs., the height of the mercury must 
be 6 feet 1^ inches. 

The same calculation is applicable to any inter- 
mediate point that may be sought, but it would be 

H 



98 CHAPTER III. 

unnecessary trouble; for, knowing the point cor- 
responding to zero, and that which corresponds to 
the maximum pressure of the instrument, we have 
only to divide the interval into equal parts, and the 
scale will be suitably graduated, having seen that 
the geiferal value of x depends solely on the cor- 
responding value of hy and is proportional to it. 

When the pressure to be measured is but slight, 
as the apparatus need not then be of very great 
height, a manometer on the above principle may be 
fixed on the engine. Thus in the experiments on 
the pressure caused by the blast*pipe, which we shall 
report hereafter, we made use of a smaU manometer 
of this kind constructed by Mr. E. Woods, engineer 
to the Manchester and Liverpool Railway Company, 
and found it act commodiously and surely. It was 
capable of marking pressures amounting to 8fi>s. 
per square inch. But to prevent the mercury from 
being driven out all at once in the sudden changes 
of pressure, or from making too great oscillations 
during the motion, recourse had been had to the 
known means of lessening the tube at the junction 
of the two branches of the syphon. This disposi- 
tion had no other inconvenience than that of sUghtly 
diminishing the sensitiveness of the instrument. 

The barometer-gauge which has just been de- 
scribed is not portative, in the case, at least» when 
it is required to measure high pressures. It must 
remain fixed to the wall where it has been once 
set up, and cannot accompany the engines in their 



OF THE PRESSURE. 99 

journey. If, the valve being once regulated, the 
^igines preserved a constant pressure throughout 
their motion, this objection would be unimportant, 
and the instrument alone would satisfy all the 
wants. The valve being fixed at the intended 
wDridng point, the corresponding pressure would 
be determined once for all, and provided no change 
were made at the spring of the valve, the pressure 
of the engine would be known at every moment of 
its work. 

But this is not the case. Nothing is more vari- 
able than the pressure of the steam during the 
motion of the engines. When, for instance, the 
valve has been regulated for 50 lbs. per square inch, 
that is, so as to begin to give issue to the steam as 
soon as the pressure shall arrive at that point, we 
are not thence to conclude that the effective pres- 
sure will never, during the motion of the engine, 
be less than 50fi>s., nor that it will never be greater. 
Both these states will occur without any change 
being made at the valve. If the steam does not 
cause the valve to blow, the only derivable con- 
clusion is that the effective pressure is under 50 fi>s. ; 
but in trying it then, either by loosening the spring 
or by the gauge, it will be found varying every 
moment according to the activity of the fire, the 
play of the pump, the inclination of the road, and 
many other circumstances apparently indifferent: 
at times the pressure will be only 15 or 18 lbs., 
then it will rise to 40 or 50 lbs. On the contrary, 



i 



100 CHAPTER III. 

if the steam is seen to blow at the valve, all that 
can be affirmed is that the effective pressure is 
above 50 lbs. But we must beware of believing, 
as at first we might be tempted to do, that because 
the valve rises as soon as the pressure reaches 
50 lbs., it from that moment gives free vent to 
the steam, and that therefore the pressure of the 
latter can in no case rise above that point. Let 
the engine in this state be submitted to the gauge, 
and it will be seen that the pressure, instead of 
being restricted to 50 lbs., may be 60 lbs., and even 
more. 

It will in effect be readily conceived that if a 
great part of the steam of the boiler escapes by 
the safety-valve, that steam can issue forth as fast 
as it is generated, only by raising the valve very 
high, in order to make for itself a sufficient passage. 
But the valve, as it rises, presses more and more on 
the spring. The latter then opposes a resistance by 
so . much the greater ; and consequently, the steam 
requires an elastic force by so much the greater, as 
it needs to create for itself a larger issue. As, 
moreover, the spring marks 50fts. only when the 
valve begins to rise, it is plain that the more its 
rising is increased, the more the corresponding 
pressure of the steam will exceed 50 fts. per square 
inch. . 

The changes of pressure which we have just 
mentioned take place during the motion of the 
engines, that is to say, while they are separated from 



OF THE PRESSURE. 101 

the stationary gauge. The latter then can no longer 
be used directly to give the pressure of the steam ; 
but, combining it with the observation of the safety- 
valve, a knowledge of the pressure may still be at- 
tained. In order to effect this, the engine must first 
be set at work, varying the starting point of the 
valve as it may appear necessary in the experiment ; 
but two things are to be carefully noted, viz., the 
point at which the valve was fixed as the starting 
point, and its subsequent rise above that point. 
The experiment being ended, the engine must be 
brought back to the stationary gauge ; then, fixing 
the valve successively at the different starting points 
which have beea taken, and producing, moreover, 
by urging the fire, the divers elevations above those 
points, which have been observed during the ex- 
periment, the degrees of pressure to which they 
correspond may be written off from the barometer- 
gauge. Thus will then be formed, for each engine, 
a register which will render it easy to pass from the 
indications of the valve, during the work, to the 
actual pressures of the steam in the engine. 

This mode, which is very practicable, is that 
which we employed when we had only the valve 
and the barometer-gauge to measure the pressure of 
the steam in locomotives ; but the portable instru- 
ments, which we are about to describe, render this 
proceeding unnecessary, and are, besides, far more 
convenient. 



102 CHAPTER III. 

Sect. II. Of the Air-gauge, 

The air-gauge is represented in fig. 17. This 
instrument, long known, but recently applied to the 
use of locomotives, consists of a tube sealed at the 
top, in which a portion of air compressed indicates 
by the more or less diminution of its volume, the 
pressure exerted on it by the steam. This tube, 
exhibited at 1 1, is terminated at the upper part by a 
ball full of air, the object of which is to expose to 
compression a greater volume of air, without how- 
ever requiring too great a length of tube. The 
tube, at the lower end, is terminated by another 
ball 6, but this is filled with mercury, which rises 
also to a certain height x in the tube. 

Near the top of the lower ball is a capillary 
aperture o, through which the steam can exercise a 
pressure on the mercury. The smaUness of the 
aperture prevents the mercury finom being easily 
spilt on conveying the instrument from place to 
place ; but it would be bett^ so to contrive as to 
be able, on occasion, to close it by means of a cock. 
In order that the lower ball may be put in contact 
with the steam, and that the upper portion of the 
instrument may still remain exposed to view, the 
tube is fixed in a metallic case, divided into two 
compartments by a horizontal partition CC; and 
the tube in traversing this partition, to whidi, 
moreover, it is hermetically sealed, has its lower 
ball enclosed in the lower compartment of the case. 



OF THE PRESSURE. 103 

and its upper part, on the contrary, in the superior 
compartment, which is opened through its whole 
length hy a longitudinal groove aadd. The case 
fixes, by means of a moveable nut, to a tap on the 
boiler, and, on the turning of a cock, the steam 
penetrates freely, by the aperture O, into the lower 
compartment of the case. It consequently presses 
on the surface of the mercury through the passage 
0, and the mercury rises in the tube till the elas- 
ticity of the compressed air, together with the 
weight of the mercury raised in the tube, equili- 
brate the pressure exerted by the steam. Divisions 
marked on the edge of the longitudinal groove will 
then indicate the corresponding pressures of the 
steam. 

The action of this instrument is founded on 
Boyle's or Mariotte's principle already explained, 
according to which the volume occupied by the air, 
under the same temperature, varies in the inverse 
ratio of the pressure which it sustains. It will 
readily be seen, in consequence, how the divisions 
of this instrument are established. 

The capacity of the upper ball of the tube must 
first be measured by taking the weight of the mer- 
cury which precisely fills it, and measuring to what 
length along the tube the same weight of mercury 
would extend ; then the capacity of the ball may be 
replaced, in the calculation, by an equivalent length 
of the tube. 

Afterwards, having introduced a certain quantity 



104 CHAPTER III. 

of mercury into the lower ball and into the tube, 
note is to be taken of the point at which the mer- 
cury stops when the instrument is exposed merely 
to the air. This point is evidently that which 
corresponds to a pressure equal to the atmospheric 
pressure, that is, to a total pressure of 14*71 Eng- 
lish pounds per square inch, or, in other words, to 
the weight of a column of mercury 30 English 
inches in height. 

This premised, in order to know the point cor- 
responding to any other pressure of the steam, let P 
be that pressure in inches of mercury, and ir the at- 
mospheric pressure similarly expressed ; let L also be 
the total length of the tube from the orifice o to the 
top, including in this measure the length of tube 
which represents the capacity of the ball filled with 
air, as has been explained above. Finally, let h be 
the height of the level of the mercury in the tube 
above the orifice o, when the instrument supports 
no more than the atmospheric pressure, and H the 
height of the same level, when the instrument is 
submitted to the pressure P. 

It has been said that the spaces occupied by the 
compressed air are in the inverse ratio of the pres- 
sures which they sustain. Now, when the instru- 
ment is exposed to the atmospheric pressure tt, 
since that pressure is then held in equiUbrio by 
the resistance of the air contained in the tube, 
plus the weight of the column of mercury whose 
height is A, it is plain that the resistance of the 



OF THE PRESSURE. 105 

air, or the pressure which it sustains, is represented 
by 

w — A. 

Similarly, the resistance of the compressed air, 
under the external pressure P, is expressed by 

P-H. 

Finally, the spaces respectively occupied by the 
compressed air, under the external pressures ir and 
P, are L — A and L — H. We have therefore the 
analogy 

L-H- 9r-A^ 

whence is derived 

L — A 
P = H + (tt - A) jj3^- 

Consequently, it will be easy, by means of this 
equation, to know the pressure which corresponds 
to a given division of the instrument; and after 
having thus determined a sufficient series of pres- , 
sures, and inscribed them on a preparatory scale, 
then by interpolation may readily be deduced there- 
from, a definitive and regular scale, indicating the 
elevations of the mercury for all the pressures 
required. 

The problem may equally be resolved in a direct 
way, without any interpolation ; that is to say, the 
elevation of the mercury corresponding to a deter- 
mined pressure^ may be found immediately ; for the 
same equation, resolved above with reference to the 



106 CHAPTER III. 

pressure P, may also be resolved with reference to 
H. It then gives 
L+P 



H=-^-i ^(L-P)^ + 4(7r-A) (L-A), 

which expresses the elevation sought. It is how- 
ever to be observed, that this equation is susceptible 
of another solution, in which the radical would be 
affected with the sign plus instead of minus. But 
the second solution, though it would satisfy the 
definitive equation of the calculation, does not apply 
to the question proposed ; for, in the case of P = w, 
the equation must give H = A, and consequently the 
radical must be affected with the sign minus^ as it is 
easy to verify. 

The value of H thus found makes known imme- 
diately the point of the scale which corresponds 
to a determined pressure P, but as that value re- 
quires a calculation somewhat complicate, the former 
method will no doubt be preferred in practice. In 
either solution, the pressure of the steam is always 
expressed by the height of an equivalent column of 
mercury. Thus in the first solution, the result once 
obtained will have to be converted into pounds per 
square inch ; and in the second solution, it will be 
requisite previously to convert the given pressures, 
from their usual expression, into an equivalent one 
in inches of mercury. But these mutations present 
DO difficulty, since it is known that a pressinre of 
14-7 1 lbs. per square inch is equivalent to a column 
of mercury of 30 inches in height. 



OF THE PRESSURE. 107 

From what has been said then, the divisions of 
the instrument may be marked for every point of 
the scale of pressures. It is however to be observed, 
that Mariotte's law, on which the preceding calcula- 
tion is founded, is exact only so long as the air 
retains the same temperature in the different states 
of €x>mpression. In order that the divisions thus 
marked should be strictly accurate, the upper part 
of the instrument, that is, the portion filled with 
air, should always remain at the temperature of the 
external air. This result is obtained to a certain 
degree, even when the pressure, and consequently 
the temperatm^ of the steam, become very consi- 
derable, because the upper part of the case Ues open 
as much as possible to the contact of the air, and 
in the rapid motion of a locomotive, the contact 
of the external air incessantly renewed, tends to 
destroy all increase of temperature that might be 
transmitted from the steam to the air compressed in 
the tube. 

In ordinary cases, then, the above-mentioned 
consideration may be dispensed with. It is clear 
however that this cause of error may easily be 
avoided, by adopting another proceeding to effect 
the graduation of the instrument. There may be 
attached first to the tube a provisional scale, divided 
merdy into very small portions, and the instrument 
thus prepared may be put on a boiler in communi- 
cation with a fixed barometer-gauge. Then as the 
barometer-gauge shall be seen to denote pressures 



i 



108 CHAPTER III. 

more and more elevated, the corresponding divisions 
of the provisional scale of the air-gauge may be ob- 
served, and consequently there will thus be formed 
a register from which the definitive scale of the 
instrument must afterwards be made out. 

Albeit, if this mode have not been used to effect 
the primitive graduation of the instrument, it is that 
at least which ought to be used to verify that gradu- 
ation, if the certainty of its accuracy be desired ; and 
it is what we have always done before employing the 
air-gauge in our experiments. Moreover, it is plain 
that when the instrument is exposed to the external 
air, the mercury ought, save the slight modifications 
that may have occurred in the barometrical pressure 
of the atmosphere, to rise in the tube to the point 
marked for the atmospheric pressure, that is to say, 
to the effective pressure zero. This is then another 
verification not to be neglected, when recourse is 
not to be had to the preceding. 

The air-gauge is portative and very commodious. 
It is usually not more than 10 inches long by an 
inch in thickness, and may be affixed with ease to 
all engines. But the divisions of the scale must be 
marked with the greatest accuracy, which presents 
some difficulty. The air too contained in the tube 
must be thoroughly free from all humidity, for that 
would become steam at the moment of the experi- 
ment. In fine, a drop of mercury lost in carrying 
the instrument, or a small quantity of water insinu- 
ated by means of the steam, into the lower ball, 



OF THE PRESSURE. 109 

may falsify the divisions. It is only then on being 
assured that the instrument is put out of hand by a 
careful workman, and as far as it may be possible, 
OD having proved it by the barometer-gauge, that 
entire confidence is to be had in its indications. 



Sect. III. Of the Thermometer-gauge. 

The thermometer-gauge is an instrument as simple 
and as portative as the preceding ; it is contained in 
a case similar to that of the air-gauge, and is simi- 
larly attached to the boiler by means of a moveable 
nut. This instrument, represented figure 19, is 
merely a thermometer, the ball of which is im- 
mersed in the boiler, and whose upper part rises 
above to expose to view the height to which the 
mercury rises. 

To establish this instrument, it evidently suffices 
to take an ordinary thermometer and to replace the 
degrees of temperature by the corresponding degrees 
of pressure, in steam in contact with the liquid, 
according to the Table which we have given in the 
preceding chapter of this work. In order however 
that the degrees thus marked should be quite exact, 
it would be necessary to protect the ball of the ther- 
mometer against the compression which the elastic 
force of the steam tends to exercise on it, by a 
double casing, and that double casing would destroy 
all the sensitiveness of the instrument. In high 
pressures, the degrees of pressure indicated by the 
scale will be found then liable to a certain inaccu- 



110 CHAPTER III. 

racy, unless, besides replacing the temperatures by 
their corresponding pressures, as has just been indi- 
cated, the latter be also corrected by taking account 
of the compression of the ball of the tube. In order 
to effect this, it will suffice to set up the instrument 
on an engine put in communication with a stationary 
barometer-gauge, and to observe, by the comparison 
of the two instruments, what correction ought to be 
made in the principal points of the scale. In this 
way will be avoided the causes of error that have 
been pointed out, and consequently the instrument 
can be verified when any doubt is entertained of its 
accuracy. We have invariably availed ourselves of 
it before using the instrument in our experiments. 

The thermometer-gauge is both portative and 
commodious, but it wants accuracy when the 
pressure of the steam suffers rapid changes, which 
is constantly happening with locomotive engines : 
the time requisite for the instrument either to 
wann or to cool to the temperature of the steam, 
will not then allow it to indicate the pressure cor- 
rectly. Another inconvenience still more serious is 
that, for high pressures, which are precisely those 
most generally wanted, the divisions are exceedingly 
small because the corresponding variations of tem- 
perature are very trifling. The instrument then be- 
comes unsure, and, in the rapid motion of the en- 
gine, almost illegible, unless its dimensions, which 
are usually about 10 inches in length, were enlarged, 
and the instrument made less commodious on that 
account. 



OF THE PRESSURE. Ill 

Sect. IV. Of the Spring-gauge or Indicator. 

The above-mentioned defects of each of the pre- 
ceding steam*gauges induce us to recommend try- 
ing, for locomotives, the use of the indicator of 
Mr. Watt, the construction of which properly fells 
into the department of engine manufacturers, where- 
as the other gauges require the aid of the optician. 

This instrument is represented figure 23. It 
consists of a small brass cylinder, similar to the 
case of the two preceding gauges, and, like them, 
fixed temporarily to the boiler. Its lower part 
contains a piston P, susceptible of rising and fall- 
ing in the cylinder, and admitting the steam to 
act imder it. The area of the piston ought to be 
precisely one square inch. On its upper part is a 
rod ^ which is maintained by a ring cc, in the 
exact direction of the axis of the cylinder. This 
rod acts against a spiral spring SS, similar to those 
of the ordinary spring-balances, and presses it with 
more or less force according as the piston is more or 
less raised by the action of the steam. A longi- 
tudinal groove aahh is made on the upper part of 
the instrument, so that an index t, moving with the 
head of the spring, juts out fi:om the groove, and 
by means of a scale engraved on the edge, indi- 
cates the pressure sustained by the spring, and con- 
sequently the effective pressure of the steam under 
the piston, that is, in the boiler. 

In order to divide the instrument, it suffices to 



112 CHAPTER III. 

withdraw the piston and ascertain its precise weight. 
It must then be put back into its place, the cylinder 
reversed, and the piston loaded at first with a 
weight of 1ft., diminished by the weight of the 
piston itself. The point at which, under this 
weight, the index rests is marked 1 ft. ; then add- 
ing successively other weights of 1ft., 2fts., &c., 
the respective points at which the index stops will 
be marked. This operation once finished, it is 
plain that when the steam shall have an elastic 
force of 1ft., 2fts., &c. per square inch, it will 
make the index rise to the corresponding points 
of the scale ; and the precaution of having in- 
cluded the weight of the piston in that of the 
first pound applied on the spring, causes the weight 
of that piston to come naturally into account in all 
cases as it ought to do. Thus the instrument will 
give immediately the pressure per square inch in 
the boiler. 

The verification visibly reduces itself to measuring 
the diameter of the cylinder and placing anew some 
weights on the piston, to ascertain that the divisions 
of the scale are exact, that the friction of the piston 
has not varied, and that the spring has presehred its 
proper elasticity. That the piston may have pre- 
cisely a square inch of surface, its diameter ought 
to be ri283 inch, or 1 inch ^ and a fortieth of an 
eighth. The omission of this latter fraction, that 
is, the use of a piston 1^ inch in diameter, would 
only cause an error of -^hj of a pound minus, which 



OF THE PRESSURE. 



113 



would make a quarter of a pound on an effective 
pressure of 50 lbs. per square inch. 



Sect. V. Comparative Table of the divers modes of 

expressing the pressure. 

As the pressure of the steam is expressed in several 
ways, and as in this work we use but one, we here 
subjoin a Table of correspondence of the divers 
modes of expressing it. 

Comparative Table of the different modes of expressing the 

pressure of the steam. 











Excess of that 










force above the 










atmospheric pres- 


ToUl 


or ibsolttte pressure of the steam | 


sure, or pressure 










called effectwe 










in high-pressore 










engines, 




in lbs. per 


in lbs. per 






in 


inch 


inch 


in inches of 


in lbs. per 


atmospheres. 


square. 


circular. 


mercury. 


square inch. 


1 


14-71 


11-55 


29-92 


*f 


1-5 


2206 


17-33 


44-88 


7-35 


2 


29-41 


23- 10 


59-84 


14-71 


2-5 


36-77 


28-88 


74-80 


2206 


3 


44-12 


34-65 


89-76 


29-41 


3-5 


51-47 


40-43 


104-72 


36-77 


4 


58-82 


46-20 


119*68 


44-12 


4-5 


66-18 


51-98 


134-64 


51-47 


5 


73-53 


57-75 


149-60 


58-82 


5-5 


80-88 


63-53 


164-56 


66-18 


6 


88-24 


69-30 


179-52 


73-53 


6-5 


95-59 


75-08 


194-48 


80-88 


7 


102-94 


80-85 


209-44 


88-24 


7-5 


1 10-30 


86-53 


224*40 


95-59 


s 


117-65 


92-40 


239-36 


102-94 



CHAPTER IV. 

OF THE RESISTANCE OF THE AIR. 

Sect. I. Of the intensity of that resistance on the 

unit of surface. 

Thb resistance of the air against the waggons 
cannot be regarded as a force to be neglected in 
calculations relative to motion on railways; for it 
is well known that trains, left to themselves, have 
at times been dragged to considerable distances by 
the mere impulse of the wind, and that engines in 
full course have literally been brought to a stand- 
still by momentary gusts of wind contrary to their 
direction. 

It is necessary then to take into account the effects 
of the resistance of the air against the trains. The 
exact evaluation however of that resistance offers 
some difficulty. Borda's experiments,^ as well as 
those of Rouse and Edgeworth,^ prove that the 
resistance of the air, within the limits which we 
have to consider, increases in the ratio of the square 
of the velocity ; and so far they are decisive : but 

^ M^moires de TAcad^tnie des Sciences, ann^ 1763. 
^ Philosophical Transactions, 1 782. 



RESISTANCE OF THE AIR. 115 

as to the absolute yalue of the resistance of the air, 
it cannot satisfactorily be determined by these ex- 
periments, because on larger surfaces being put to 
trial, there resulted resistances greater per unit of 
surface, leaving thus a doubt as to the choice to be 
made between these different results. 

Nevertheless, till very lately, the only mode of 
estimating the resistance of the air was by the 
determinations of Borda. A work, but little known 
as yet, that of M. Thibault,^ has however appeared, 
and furnished much more precise data on the sub- 
ject. 

Borda's experiments had been made in a circular 
motion, and Dubuat ^ had already thought that the 
singular anomaly which they presented, to wit, that 
of resistances increasing in a greater ratio than the 
surfaces, must proceed from the nature of the cir- 
cular motion itself. He had in fact observed, that 
a body set in motion in a fluid always draws a 
portion of the fluid after it, and that this portion 
of fluid, attached to the moving object, is inces- 
santly disturbed and driven back by the molecules 
of fluid which, after having sustained the shock of 
the moving surface, escape around its edges and 
rush behind it. There will always then be pro- 
duced a partial vacuum, or diminution of pressure. 



^ Experiences but la resistance de Fair, par M. Thibault, lieu- 
tenant de Vaisseau, Brest. 
* Principes d'Hydraulique. 



116 CHAPTER IV. 

or, as Dubuat has termed it, a non-pressure^ behind 
the moving body; and as the definitive resistance 
against that body, is nothing else but the difference 
of the pressures exerted by the air against the 
front and hind surfaces, it follows that the re- 
sistance of the air against a moving body will always 
be increased, whenever the diminution of pressure 
behind the body shall become more considerable. 
Now if we suppose a surface of a given magnitude, 
set in motion in a straight line, there will be caused 
behind it a non-pressure, and the resistance suffered 
by the moving body will be the difference between 
the pressure of the air in front and the diminished 
pressure which subsists behind. If, after this, the 
body be submitted to a circular motion, it is evident 
that in proportion to the greater curvature of the 
Une described by the body, the air, after passing over 
its edges, wiU by so much the more disturb the portion 
of fluid which follows it, and thus the pressure be- 
hind will be diminished; whence will result a greater 
resistance against the moving body. Again, if the 
latter be brought nearer the centre of motion, this 
same effect will be augmented. Definitively then, 
the resistance against a given surface, in a circular 
motion, will become greater as the surface is nearer 
to the centre of rotation ; and in order that two 
surfaces of different magnitudes have to contend 
with an equal degree of disadvantage, — in other 
words, that the resistance of the air, per imit of 
surface, be the same for each, — those two surfaces 



RESISTANCE OF THE AIR. 117 

must be placed at distances from the axis, propor- 
tional to the sides of the squares which represent 
them. 

This in effect has been verified by the experi- 
ments of M. Thibault^ which have demonstrated, 
that in a circular motion, the apparent augment- 
ation of the resistance of the air against large 
surfaces, compared with smaller ones, arises merely 
from the fact of their not being removed to a dis- 
tance from the axis, proportional to the length of 
their side ; that, subjected to this condition, the 
large surfaces, as well as the small, experience resist- 
ances really proportional to their extent ; and that 
when non-subjected to this condition, the greater 
surfaces, on the contrary, may have to overcome 
resistances, per imit of surface, double those op- 
posed to the surfaces of smaller extent. It is then 
to be concluded from those experiments that the 
circular motion cannot, with any accuracy, be used 
in determining the resistance of the air in a direct 
motion, unless the surfaces employed be of very 
small extent compared to the length of the radius 
of rotation. 

The experiments of the same author confirm, 
moreover, two results already obtained by Dubuat 
with respect to liquids, and indicated by him with 
respect to fluids. The first of these results is, 
that the resistance against a body moving in an 
indefinite fluid, at rest, is less than the resistance 
experienced by the same body placed at rest in an 



118 CHAPTER IV. 

indefinite fluid moving against it, which seems to 
denote that a fluid in motion separates itself less 
easily than a fluid at rest. The second is, that a 
thin plate meets with a greater resistance from the 
air than a prismatic body presenting in front the 
same surface, and that the resistance diminishes 
according as the prism is longer. This circum- 
stance is occasioned thus : the air having glided 
over the edges of a thin body, rushes immediately 
behind it with great rapidity, and carrying in its 
motion the portion of fluid, which we have men- 
tioned above, produces a relative vacuum behind 
the opposed surface. But if the moving body be a 
lengthened prism, the air in passing along its sides 
loses a certain portion of its acquired velocity, and 
consequently, on reaching the hind face of the 
prism, extends itself behind it with a force more 
and more moderated ; whence results that it pro- 
duces there a partial vacuum, or non-pressure, less 
considerable than in the case of a simple sur&ce. 
And as we have seen that the definitive resistance 
against a moving body is the difierence between the 
pressure of the air in front and the partial vacuum 
created behind, it follows that longer bodies de- 
finitively suffer from the air a less resistance than 
bodies of inconsiderable thickness. 

Besides, the experiments of M. Thibault have 
confirmed those of Borda, on the proportionality of 
the resistance of the air to the square of the ve- 
locity, within the limits of velocity that we have 




RESISTANCE OF THE AIR. 119 

to consider in this work. They have, moreover, 
demonstrated that if two square surfaces be placed 
so that one shall precisely screen the other, and at 
a distance apart equal to one of their sides, the 
resistance against the screened surface will be 
7-tenths of the resistance suffered by the surface in 
front. It consequently results that, when two sur- 
faces are separated by a considerable space relatively 
to their extent, the resistance of the air against the 
second is to be estimated nearly as if it were iso- 
lated in the air; but if, on the contrary, the two 
surfaces are very near each other, relatively to their 
extent, there is room to think that the screened 
surface may be almost entirely protected against the 
effect of the air, since a space equal to one side of 
the surface would be requisite for the air to exert 
against it a resistance equal to two-thirds of the re- 
sistance against an isolated surface. 

Finally, uniting the results obtained by Borda, 
Dubuat, and M. Thibault, and limiting ourselves to 
the case of a body moving in the air at rest, which 
is the only case that occurs in this work, we have, 
to determine the resistance of the air, the following 
formulae, in which S represents the front surface of 
a body traversing the air in a direction perpen- 
dicular to that surface, V the velocity of the motion, 
e a co-efficient variable with the length of the body, 
and, lastly, Q the definitive resistance produced by 
the air against the body. 



120 CHAPTER IV. 

Q= 0011896 € ^ V^ . . Resistance of the air ex- 
pressed in English fts., 
the surface S being ex- 
pressed in square feet, 
and the velocity V in 
English feet per second. 

And in applying these formulae it will be necessary, 
according to the case, to give to the letter e the 
following values : 

for a thin surface 6= 1*43 

for a cube e=ri7 

for a prism of a length equal to 
three times the side of its 
front surface 6=1 '10 



Sect. II. Of the resistance of the air against the 
waggonSy isolated or united in trdins. 

From what we have just seen, it will be easy to 
estimate the resistance of the air against a prismatic 
body in motion, when its front surface and dimension 
in length are known. But as a waggon does not 
present a regular prismatic form, it becomes neces- 
sary first to consider how we may find what surface 
it really offers to the shock of the air. 

The front surface of a waggon may be directly 
measured; it consists of two distinct parts, the 
surface of the load and that of the waggon itself. 



RESISTANCE OP THE AIR. 121 

The former of these surfaces necessarily varies 
according to the nature of the goods which form 
the load; and as to the surface of the waggon, 
properly so called, on railroads of 4 feet 8^ inches 
width of way, and for waggons with a single plat- 
form, it usually amounts to 14'33 square feet. But 
this is evidently not the only surface against which 
the air exerts its resistance ; for the spokes of the 
wheels cannot turn rapidly as they do, during the 
motion, without meeting with a certain resistance 
from the air ; and again the axle-trees, axle-boxes, 
springs, and hind-wheels of the waggon, are sepa- 
rated far enough from the similar pieces which 
precede them, not to be considered as wholly pro- 
tected against the shock of the air. 

Considering separately a wheel of 3 feet in diameter, 
like that of the ordinary waggons, and reducing the 
surface of all its spokes, whose divers points have dif- 
ferent velocities according to their distance from the 
centre, to the surface which, being moved at the ve- 
locity of the circumference of the wheel, would suffer 
from the air an equivalent resistance, each wheel is 
found to offer in this respect a surface of 1 *25 square 
feet. Adding then the direct surface offered by the 
nm of the wheel seen in front, as well as by the naves, 
axles, and springs, we arrive at this result, that each 
pair of wheels presents to the shock of the air a 
total surface of 7*03 square feet. Now, if we con- 
sider, either in an isolated waggon or in a train 
composed of several waggons, every pair of wheels 



122 CHAPTER IV. 

except the first, we shall observe that all present 
that extent of surface to the shock of the air ; but 
as the whole of that surface is screened, to wit, the 
spokes by those which precede them in the motion, 
and the wheels, naves, and axles, by the similar 
pieces in the pair of wheels preceding them, we 
shall approximatively take this circumstance into 
account by assimilating the effects of the air on 
these successive pieces, to those observed by M. 
Thibault in the case of surfaces screened by each 
other and separated by an interval equal to the side 
of their square, which is not far from the truth in 
the case under consideration. We shall then reduce 
the above surface to two-thirds, and shall -thus have 
4*69 square feet, for the direct surface opposed to 
the shock of the air during the motion of the 
waggons, by each pair of wheels exclusive of the 
first. 

Now, as to the fore- wheels of the first waggon, 
the surface of projection of the rims, springs, &c., is 
already reckoned in the total front surface of the 
waggon, but account must also be taken of the 
rotation of the spokes, which for this pair of wheels 
reduces the number 4*69 to 1*67 square feet. It 
follows then firstly that, for an isolated waggon, the 
addition to be made to its front surface, or rather to 
its surface of projection directly measured, for the 
fore and hind-wheels, should be 6 square feet. Fur- 
thermore, for the same case, as a loaded waggon 
presents, at a medium, a length equal to once and a 



RESISTANCE OF THE AIR. 123 

half the square root of its front surface, we should 
in the preceding formulae make 6 = 1*15. 

As to the trains of several waggons, we at first 
see that, for the resistance of the wheels, an addition 
must be made to the transverse section of the train, 
of 9 square feet per intermediary waggon and of 6 
square feet only for the first ; but as the waggons 
composing the same train, though very near each 
other, are not however in contact, it is necessary 
further to seek upon what extent of surface, these 
waggons thus united still suffer the resistance of the 
air during their motion. 

In order to effect this, we operated in the following 
manner : 

On the 3rd of August, 1836, accompanied by 
Mr. E. Woods, engineer of the Liverpool and Man- 
chester Railway, we took five waggons, of different 
heights, loaded with goods, and measured their 
front surfaces. These waggons were then drawn 
to the incUned plane of Whiston, an exact section 
of which will be given in the following chapter. 
They were then abandoned, separately, to their own 
gravity, and as the inclination of the plane was suf- 
ficient to decide their motion, they ran down of 
themselves, and having passed the foot of the plane, 
continued their motion along another plane much 
less inclined than the former, till they were brought 
to rest by the retarding forces, namely, the friction 
proper to the waggons themselves and the resistance 
of the air against their surface. After the waggons 



124 CHAPTER IV. 

had been submitted separately to this experiment, 
they were brought back on the inclined plane to 
the point from which they had first started, and 
again abandoned to gravity, but all united in one 
train. 

As the friction proper to the waggons had evi- 
dently not varied, it is clear that if the latter 
experiment gave a total resistance greater than the 
sum of the frictions of the five separate waggons, 
augmented by the resistance of the air against the 
transverse section of the train, the surplus must be 
attributed to the indirect shock of the air against 
the successive surfaces of the intermediary waggons 
of the train ; and, consequently, a valuation of that 
efiect was to be obtained. 

We shall explain, in the following chapter, in 
what manner the friction of the waggons was 
concluded from the circumstances of their motion 
on the two inclined planes ; in this place it will 
suffice to relate the results of six experiments, made 
with a special view to determine the resistance of 
the air against the intermediary waggons. In the 
following Table, which contains these results, we 
give, for the first five experiments, the weight of 
each waggon and the surface it opposes to the 
shock of the air, including the wheels and accessory 
pieces, as has been indicated above.'^ In experi- 

* When these experiments were published for the first time, an 
error had slipped into the measm'e of the front surface of the 
frame- work of the waggons ; which error is corrected here. 



RESISTANCE OF THE AIR. 125 

ment VI., made on the waggons united, the surface 
carried into the eighth column is successively : first, 
that of the highest waggon of the train, augmented 
by the surface representing the resistance of the 
wheels and the screened parts ; and, afterwards, the 
surface which gives, for the five waggons together, 
a friction equal to the sum of the frictions of the 
five waggons separate. The other columns make 
known the circumstances of the experiment, and 
consequently determine the friction of the waggons, 
as will be seen in the following chapter. To cal- 
culate the resistance of the air, we have taken in 
the case of the separate waggons €=1'15, as has 
been said above ; and for the case of the connected 
waggons, as they formed a prism of a length equal 
to seven times its width, we have taken, according 
to the observations of Dubuat, 6= 1*07. 

During these experiments the weather was fine, a 
slight air was perceptible in the contrary direction 
of the motion, but its action was so weak that a 
wind-gauge, exposed in an open place, could give 
no appreciable valuation of it. 

As to the mode of experiment here employed, we 
must say, that when the resistance of the air against 
the front surface of the trains only is considered, it 
may appear that during the descent of the five 
waggons united, they must have pressed strongly 
one against the other, because the shock of the air, 
which was the resistance, exerted its effort against 
the front, whereas the gravity, which was the mo- 



126 CHAPTER IV. 

tive force, acted nearly in the centre of the mass in 
motion. Hence, therefore, it might be concluded, 
that this pressure of the waggons one against the 
other would throw them out of square upon the 
line, and consequently, in this case, make their 
friction appear greater than it really was. But it 
must be observed, that in experiment VI. the wag- 
gon of greatest section was put last in the train, 
and again, that the resistance of the air exerted 
itself against each mtermediate waggon, which di- 
vided that resistance over the different points of the 
train, instead of concentrating it on the front sur- 
face. Moreover, a pressure of the wagons one 
against the other may, in effect, throw them out of 
square when they are connected by stiff bars, be- 
cause the shortening of the train then tends to set 
those bars across, and thus drive the wagons against 
the rails on either side. But the waggons here em- 
ployed were not of this kind; they were joined 
together merely by chains, and in that state the 
mutual contact took place by the projecting ends of 
the frame on each side; consequently, it could 
only tend to maintain them more directly on the 
road, since, in such a system of junction, the 
shortest line the train can form, or that which is 
determined by the pressure of the hinder waggons, 
is not a crooked line as in the case of the stiff bars, 
but a straight and direct line from one end of the 
train to the other. None of these accessory effects 
then occurred in the experiments which we are 
about to report. 



RESISTANCE OF THE AIR. 



127 



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128 CHAPTER IV. 

From this Table it appears, that limiting our- 
selves in experiment VI., to taking account of the 
resistance produced by the rotation of the wheels 
and by the screened pieces of the frame-work of 
the waggons, the friction of the five waggons de- 
duced from this experiment, seems to be more 
considerable than the sum of the frictions of the 
same five waggons, deduced from the preceding 
experiments ; and that it is only by adding 3 square 
feet more to the surface exposed to the shock of 
the air in experiment VI., that we are enabled to 
put the result of that experiment in harmony with 
those of the separate waggons. We must then 
conclude, that besides the resistance opposed by 
the air against the wheels and the screened pieces 
of the frame- work, there was still a surface of 3 
square feet for the four waggons which followed 
the first, or a surface of 1 square foot per waggon, 
exposed to the shock of the air during the motion. 
That is to say, the air after the passage of the 
first waggon, rushed between that waggon and the 
following one, and notwithstanding the small in- 
terval which separated them, it still exerted on the 
second waggon a certain action, the intensity of 
which might be represented by the shock of the 
air against 1 square foot of direct surface. 

Consequently, adding this new surface to that 
already obtained to represent the motion of the 
wheels and accessory pieces, we see that when a 
train of waggons is in motion on a railway, it is 



RESISTANCE OF THE AIR. 129 

necessary, in order to estimate the effects of the 
resistance of the air against its progression, to take 
as resisting surface that of the waggon of greatest 
section, augmented by 10 square feet per interme- 
diary waggon, and by 6 square feet for the first 
waggon, including of course in this number the 
engine itself and its tender. 

On railways of about 5 feet width of way, the 
surface of the highest waggon may at a medium be 
reckoned at 70 to 74 square feet ; we may then 
esteem, in general, the resisting surface of a train 
of waggons at 70 square feet, plus as many times 
10 feet as there are carriages in the train, including 
the engine and its tender. If the train consists 
of diligences, as their surface is from 60 to 64 
square feet, then in the preceding estimation the 
number 70 must be replaced by the number 60. 

If the road has a wider way, or if the carriages 
ofier a surface difibrent from that we have just 
indicated, the carriage of greatest section must be 
measured, and that measure used, instead of the 
number 70 or the number 60 of the above calcu- 
lation. If the wheels of the waggon are more than 
3 feet in diameter, there will likewise be an addition 
to make, to take account of the greater surface 
which they expose to the shock of the air during 
the motion. This addition would be about 3 square 
feet per waggon, for wheels of 5 feet in diameter 
instead of 3. Finally, if the interval between the 

K 



130 CHAPTER IV. 

waggons, instead of being about 2 feet, as it was 
in experiment VI., and as it is at a medium on 
ordinary railways,^ considering the diflferent kinds 
of carriages and the inequalities of their loading, 
were augmented by any important quantity, there 
might also be some addition to make for the effect 
of the air against the loads of the successive 
waggons ; but as our determination in this respect 
gave something less than 1 square foot per waggon, 
and as the interval between the waggons could not 
be augmented by any thing considerable without 
being liable to inconveniences in practice, we deem 
that 1 square foot per waggon may comprehend 
nearly all cases. 

When the effective surface presented to the shock 
of the air shall be known by the preceding calcula- 
tion, it must be substituted for the letter S in the 
formulae given above, putting at the same time for c, 
its value suitably to the length of the prism formed 
by the train of waggons. According to the vari- 
ation of € observed by Dubuat for prisms of divers 
proportions, it will be found that in the case of a 
train of 5 waggons, we must make € = 107, and 
that the case of a train of 25 waggons would require 
e = l-04. In order then not to have to return 
continually upon these considerations we will take 
as a medium 6 = 1*05, which is suitable to a train 
of 15 waggons, and expressing at the same time, 
in the formula given above, the velocity in miles 



RESISTANCE OF THE AIR. 131 

per hour, we shall have, in fine, to express the 
resistance of the air against a train of waggons in 
motion, the following formula : 

Q = 002687 S v^ . . . Resistance of the air, in 

pounds, the effective sur- 
face of the train or the 
quantity S being expressed 
in square feet, and the ve- 
locity of the motion in 
miles per hour. 



Sect. III. Table of the resistance of the air against 

the trains. 

To dispense with all calculation relative to the 
resistance of the air, we here subjoin a Table show- 
ing its intensity, for all velocities from 5 to 50 miles 
per hour, and for surfaces of from 10 to 100 square 
feet. Were it required to perform the calculation 
for a velocity not contained in the Table, it would 
evidently suffice to seek the resistance corresponding 
to half that velocity and to multiply the resistance 
found by 4 ; or, on the contrary, to seek the re- 
sistance corresponding to the double of the given 
velocity, and to take a quarter of the result. So, 
the resistance of the air against a surface of 100 
square feet, at the velocity of 50 miles per hour, is 
equal to four times the resistance of the air against 
the same surface, at the velocity of 25 miles per 



132 CHAPTER IV. 

hour. As to surfaces greater than 100 square feet, 
they must be decomposed into surfaces less than 
100 feet, and then the Table will still give the 
results required; for the resistance against a sur- 
face of 120 square feet is evidently nothing more 
than the sum of the resistances against one surface 
of 100 square feet and one of 20 square feet. 

By means of the Table in question will be obtained, 
without calculation, the resistance of the air expressed 
in pounds, for any velocity of the moving body ; but 
it is to be observed, that the Table supposes the 
atmosphere at perfect rest. If then there be a wind 
of some intensity, favourable to the motion or con- 
trary to it, account must be taken thereof. In order 
to effect this, it will suffice to observe that if the wind 
is favourable, the body will move through the air 
only with a velocity equal to the differ^ice between 
its own absolute velocity and that of the wind ; and 
that if, on the contrary, the wind is opposed to the 
motion, the effective velocity of the body through 
the air will be equal to the sum of its own velocity 
augmented by that of the wind. In this cai&e, then, 
the velocity of the wind must first be measured, by 
abandoning a light body^ to its action, and noting the 
time in which it traverses a space previously mea- 
sured on the ground ; or else an anemometer may 
be used for the purpose. Then the velocity of the 
wind must be subtracted from that of the train in 
motion or added to it, according to the case ; and 
that difference or that sum is the velocity to be 



RESISTANCE OF THE AIR. 133 

sought in the Table, or substituted in the formula, 
to obtain the corresponding resistance against the 
whole train. 

If the wind, instead of being precisely contrary or 
favourable to the motion, should exert its action in 
an oblique direction, it would tend to displace all the 
waggons laterally ; and consequently, from the coni- 
cal form of the wheels, all those on the farther side 
from the wind would turn on a larger diameter than 
those on the side towards the wind. The resistance 
produced will therefore be the same as that which 
would take place on a curve on which the effect of 
the centrifugal force were not corrected, and that 
resistance would necessarily be very considerable; 
but as we have made no experiment on this subject, 
we shall not dwell on it any longer here. 



134 



CHAPTER IV. 



Practical Table of the resistance of the air against the 

trains. 



Velocity of 
motion, in 
mUes per 


Resistance 
of the air, 
in lbs. per 
square foot 


Resistance of the air, in pounds ; the effective 
surface of the train, in square feet, being : 




















hour. 


of surface. 


20 


30 


40 


50 

tbs. 


60 

tbs. 


70 
tbs. 


80 
tbs. 


90 
lbs. 


100 

tbs. 


miles. 


lbs. 


ibs. 


tbs. 


lbs. 


5 


•07 


1 


2 


3 


3 


4 


5 


5 


6 


7 


6 


•10 


2 


3 


4 


5 


6 


7 


8 


9 


10 


7 


•13 


3 


4 


5 


7 


8 


9 


11 


12 


13 


8 


•17 


3 


5 


7 


9 


10 


12 


14 


15 


17 


9 


•22 


4 


7 


9 


11 


13 


15 


17 


20 


22 


10 


•27 


5 


8 


11 


13 


16 


19 


22 


24 


27 


11 


•33 


7 


10 


13 


16 


20 


23 


26 


29 


33 


12 


•39 


8 


12 


15 


19 


23 


27 


31 


35 


39 


13 


•45 


9 


14 


18 


23 


27 


32 


36 


41 


45 


14 


•53 


11 


16 


21 


26 


32 


37 


42 


47 


53 


15 


•60 


12 


18 


24 


30 


36 


42 


48 


54 


60 


16 


•69 


14 


21 


28 


34 


41 


48 


55 


62 


69 


17 


•78 


16 


23 


31 


39 


47 


54 


62 


70 


78 


18 


•87 


17 


26 


35 


44 


52 


61 


70 


78 


87 


19 


•97 


19 


29 


39 


49 


58 


68 1 78 


87 


97 


20 


1-07 


22 


32 


43 


54 


65 


75,' 86 


97 


107 


21 


1-19 


24 


36 


47 


59 


71 


83 


95 


107 


119 


22 


130 


26 


39 


52 


65 


78 


91 


104 


117 


130 


23 


1-42 


28 


43 


67 


71 


85 


100 


114 


128 


142 


24 


1-55 


31 


47 


62 


78 


93 


109 


124 


140 


155 


25 


1-68 


34 


50 


67 


84 


101 


118 


134 


151 


168 


26 


1^82 


36 


55 


73 


91 


109 


127 


146 


164 


182 


27 


1^96 


39 


59 


78 


98 


118 


137 


157 


176 


196 


28 


211 


42 


63 


84 


106 


127 


148 


169 


190 


211 


29 


2-26 


45 


68 


90 


113 


136 


158 


181 


203 


226 


30 


242 


48 


73 


97 


121 


145 


169 


194 


218 


242 


31 


2-58 


52 


77 


103 


129 


155 


181 


206 


232 


258 


32 


2-75 


55 


83 


110 


138 


165 


193 


220 


248 


275 


33 


2-93 


59 


88 


117 


147 


176 


205 


234 


264 


293 


34 


3-11 


62 


93 


124 


156 


187 


218 


249 


280 


311 


35 


3-29 


66 


99 


132 


165 


197 


230 


263 


296 


329 


36 


3-48 


70 


104 


139 


174 


209 


244 


278 


313 


348 


37 


3^68 


74 


110 


147 


184 


221 


258 


294 


331 


368 


38 


3-88 


78 


116 


155 


194 


233 


272 


310 


349 


388 


39 


4^09 


82 


123 


164 


205 


245 


287 


327 


368 


409 


40 


4^30 


86 


129 


172 


215 


258 


301 


344 


387 


430 


41 


4-52 


90 


136 


181 


226 


271 


316 


362 


407 


452 


42 


4-74 


95 


142 


190 


237 


284 


332 


379 


427 


474 


43 


4-97 


99 


149 


199 


249 


298 


348 


398 


447 


497 


44 


6-20 


104 


156 


208 


260 


312 


364 


416 


468 


520 


45 


5-44 


109 


163 


218 


272 


326 


381 


435 


489 


544 


46 


569 


114 


171 


228 


285 


341 


398 


455 


512 


569 


47 


5-94 


119 


178 


238 


297 


356 


416 


475 


535 


594 


48 


619 


124 


186 


248 


310 


371 


433 


495 


557 


619 


49 


6-45 


129 


194 


258 


323 


387 


452 


516 


581 645 


50 


6-72 


134 


202 


269 


336 


403 470 

1 


538 


605 672 

1 



CHAPTER V. 

OF THE FRICTION OF THE WAGGONS ON 

RAILWAYS. 

Sect. I. Necessity of new inquiries on this subject. 

From the description we have given of the engine, 
it has been seen that the steam, acting on the 
pistons, communicates to the wheels a rotatory 
motion, which must infaUibly propel the engine, 
provided the train which follows it do not oppose 
a resistance greater than the force it commands. 

An important inquiry then, as to the motion of 
locomotives, consists in determining the resistance 
caused by the trains which they have to draw. 

These trains are formed of a number more or less 
considerable of carriages called waggons, which are 
loaded with goods. Their resistance to the motion 
depends not only on their weight, but on the state 
of the railway and on the more or less perfect con- 
struction of the carriages. The object -in view in 
the making of a railway being to produce a road per* 
fectly hard and smooth, on which the carriages shall 
roll easily, if the railway happen to be indifferently 
maintained or otherwise to deviate from the con- 
ditions for which it has been estabUshed, it is plain 



136 CHAPTER V. 

that the resistance opposed by the train along the 
rails will be by so much the greater. The same will 
occur if the carriages, from defective construction or 
want of repair, have a considerable friction. 

This observation shows that the force necessary 
to move a given weight, a ton for instance, may not 
be always the same, either on all railways, or with 
all kinds of carriages. On rails perfectly even, and 
with waggons well constructed and well greased, the 
draught of a ton may require a force of but 6 fts. 
We mean that a weight of 6fts. suspended by a 
cord over a pulley, would suffice in this case to 
move, or at least to maintain in motion, a carriage 
weighing a ton. On another railway, on the con- 
trary, and with carriages of a different construction, 
the same load of a ton may require a much greater 
force. 

The old waggons on which some experiments had 
been made, were supposed to require a force of 
10 or 12 lbs. for each ton of weight of the load. 
They had afterwards been improved, but had not 
been submitted to any experiment made on a large 
scale and in the regular working state. On the first 
introduction of the new waggons, an essay was 
indeed made on a single one and at the moment it 
left the workmen's hands. But as this waggon had 
been carefuUy oiled expressly for the trial ; as it had 
as yet received no shock to bend the axle-trees, or to 
throw the wheels out of square ; as the wheels were 
new and perfectly round ; as, in fine, the rails had 



FRICTION OF THB WAGGONS. 137 

been carefully swept for the purpose, the result 
of such an experiment could hardly be considered 
as a practical result. So, on the Liverpool Railway, 
the friction of the trains was still valued at lOfts. 
per ton. 

These uncertain data could not suit a new work, 
or calculations made on modern waggons ; and 
therefore we undertook, in order to determine the 
friction of waggons, the series of experiments which 
we are about to relate. 



Sbct. II. Of the friction of waggons determined by 

the dynamometer. 

The most natural means of attaining the determi- 
nation of the friction or resistance of the waggons 
seemed to be to employ the dynamometer, since it 
gives immediately the force of traction necessary to 
effect the motion ; but, as the action of drawing, 
whether by men, or any other animated mover, is 
performed by pulls, the dynamometer merely oscil- 
lates between limits wide apart, and can give no 
certain result. It appeared to us, however, that if 
the traction were performed by an engine whose 
strain is always equal, and whose motion too is 
regulated by the mass of the train itself, the 
dynamometer would, perhaps, have but slight os- 
cillations, and that the pulsations of the engine 
would be insensible, especially on the hinder car- 
riages. 



138 CHAPTER V. 

For this reason, at the moment the engine Leeds 
started with a train of twelve waggons, when the 
whole mass was set in motion, and that motion 
continued at the uniform velocity of about three or 
four miles per hour, the drawing chain of the last 
three waggons was detached and replaced by a cir- 
cular spring-balance, previously disposed for the 
purpose. The rod of the balance was fixed to the 
hinder part of the ninth waggon, and the three 
following ones, which were the last of the train, 
were fastened to the spring. The experiment took 
place on the half mile from 1 ^ to 2 of the Liverpool 
and Manchester Railway, on a space which is exactly 
level. 

We expected to see the balance nearly invariable ; 
we were, however, deceived. The style maintained 
itself most frequently about the point marking 
100 lbs., but it was continually subject to great 
variations, which went from 50 lbs., the least, to 
170fts., the greatest; and even, in a sort of ex- 
traordinary pull, which the engine gave at times, 
the needle was seen to fly to the end of the balance, 
which indicated 220 lbs. The latter case, however, 
only occurred accidentally, and immediately after 
the needle returned to its habitual point of about 
100 lbs., and resumed its oscillations between 50 9>s. 
and 170 lbs. After having waited in vain to see 
the motion regulate itself in a. more steady manner, 
it appeared to us that the experiment was not sus- 
ceptible of greater precision. 



FRICTION OF THE WAGGONS. 139 

The variation of the needle between 50 lbs. and 
170 lbs. gave the medium of 110 lbs., and the three 
waggons weighed together 14*27 tons; thus the 

experiment gave ittot" ^^ 7*70 lbs. of resistance per 

ton. But, as this mean was much too uncertain, it 
appeared necessary to recur to another mode of 
experiment. 

In consequence, a convenient spot being chosen 
on the Liverpool and Manchester Railway, near the 
foot of the Sutton inclined plane, at the distance of 
1 1^ miles from Liverpool, the level of it was taken 
with strict accuracy in tenths of an inch, and the 
experiments were begun on the principle we are 
about to explain. 



Sect. IIL Of the friction of carriages^ determined 
by the circumstances of their spontaneous descent 
and stop upon two consecutive inclined planes. 

Suppose a system of two wheels joined together 
by an axle-tree fixed invariably to each (fig. 31), 
and loaded with a given weight resting at N, on a 
chair on which the axle-tree may turn freely. Let 
this system be placed on an inclined plane, along 
which it is liable to roll. Again, at the foot of the 
first plane, let there be another inclined plane con- 
tinuing the former, and on which the rolling body 
may continue its motion. Finally, suppose that the 



140 CHAPTER V. 

former of the two planes be sufficiently inclined to 
cause the body placed upon it to roll down spon- 
taneously, and by its own weight; and that the 
second, on the contrary, though descending in the 
same direction, be so slightly inclined that the 
body, were it simply placed upon it, would be kept 
still by the friction. 

In these circumstances it is plain that the body, 
abandoned to itself, will first roll down the first 
inclined plane, accelerating its velocity gradually, 
and that on reaching the second plane, its motion, 
on the contrary, will slacken by degrees, till having 
exhausted its acquired velocity, it finally be brought 
to rest. 

K the body experiences a considerable friction, it 
will assume little velocity in its descent on the first 
plane, and will promptly come to a stand on the 
second. If, on the contrary, the friction has but 
little intensity, the body will acquire a great ve- 
locity on the first plane, and will prolong its course 
considerably on the second. Comparing, then, the 
height which the body has descended, with the 
distance it has traversed before stopping, it will be 
possible to recognise what intensity of friction it has 
been submitted to in its course. 

To obtain an analytical relation giving the so- 
lution of this problem, it will be proper first to 
form the equation of the motion of the body on the 
two planes, and therefrom to deduce the velocity 



FRICTION OF THE WAGGONS. 141 

it will acquire in descending the first plane, and the 
distance it will traverse on the second, in virtue of 
that velocity. 

Hence, the inquiry will comprise three successive 
questions: 1st. To determine the effective accele- 
rating force to which the centre of gravity of the 
system will be subject in its motion ; 2nd. To de- 
duce from this the velocity acquired by the moving 
body at the foot of the first plane ; and 3rd. To 
conclude finally the distance it will have traversed 
on the second plane at the moment when the 
friction shall have reduced its velocity to nothing. 

The determination of the effective accelerating 
force required, will be effected by means of the 
principle that the motive forces applied and ef- 
fective must be in equilibrio, that is to say, must 
have their resultants equal and opposed, as well as 
their momenta equal and opposite when the effective 
forces are taken in the contrary way to their di- 
rection. 

Now, the motive forces applied to the system, 
are : 

1st. The weight of the body of the waggon 
resting on the chair of the axle-tree, and which we 
will call P. This force, acting vertically, will de- 
compose into two others : one, in the direction of 
the plane, will have an inunediate effect, and will 
draw the body along the plane ; the other, per- 
pendicular to the direction of the plane, will pro- 
duce a pressure of the chair upon the axle and of 



142 CHAPTER V. 

the rim of the wheel upon the rail, and will conse- 
quently cause on each of these points a friction, of 
which we shall presently express the effect. If we 
call & the angle of the plane with the horizon, the 
first of these two forces will be P sin. 6\ and the 
second P cos. ff ^ and the two together may replace 
the primitive force P. 

2nd. The weight of the system of the two rolling 
wheels, with their axle. We will call this force 
p, and will also replace it by two others p sin. d* 
and 'p COS. 6i the one parallel, the other normal to 
the plane. 

3rd. The adhesion of the wheel on the rail at T. 
This force acts along the plane contrariwise to the 
motion oi translation. It is this force which pro- 
duces the rotation of the wheel, by preventing its 
circumference from sliding without turning during 
the motion along the plane. We will express this 
force by the weight T, which shall be equivalent 
to it. 

4th. The resistance of the air against the surface 
of the system set in motion. Experience has de- 
monstrated that this force is proportional to the 
square of the velocity, and we will, in consequence, 
express it by Qi;*, Q being the weight which re- 
presents its intensity against the known surface of 
the moving mass, in the case of 1;= 1 . 

5th. The normal force P cos. dl which has been 
mentioned above, produces a pressure of the chair 
against the axle, and thus its effect will be to cause 



FRICTION OF THE WAGGONS. 143 

a friction at the point of contact. But as expe- 
rience has proved that the friction of bodies sliding 
on each other is a force proportional to the pres* 
sure, and independent of the velocity or the extent 
of the surfaces in contact, we will express the 
friction in the present instance by f P cos. dl f 
being a constant quantity; and that force will act 
tangentially to the circumference of the axle, and in 
the direction contrary to the motion of rotation. 

6th. Lastly, the same force P cos. 6l and more- 
over the force 'p cos. 6' produced by the weight of 
the wheel, will exert a pressure at the point of 
contact T of the wheel on the rail. There will 
result from this pressure a friction at T ; but as at 
this point the two surfaces in contact do not slide, 
but merely roll one upon the other, the friction 
produced will be of the second species. And, as it 
is known from Coulomb's experiments, that the 
intensity of this friction is inversely as the diameter 
of the wheel, we will express it by 

/'(P+ii)cos. «'X-^; 

f being a constant quantity, which is easily de- 
duced from the direct experiments made on this 
subject, with wheels of 3 feet diameter, or of 1*5 
feet radius. This force, in fine, will act tangentially 
to the circumference of the wheel, and contrarily to 
the motion. 

Such are the divers motive forces applied to the 
svstem. 



144 CHAPTER V. 

On the other hand, if we express by g the 
gravity ; by ^ the effective accelerating force which 
produces the motion of translation of the centre c 
of the wheel ; by -^ the effective accelerating force 
which produces the rotation of a point of the wheel 
situated at the distance 1 from the axle, and, in 

fine, by -&^ the momentum inertise of the wheel, 

it is plain that the mass of the body being > 

the effective motive force which produces the motion 
of translation will he 

and the momentum of the effective motive force of 
the motion of rotation, will be 

9 ^ 

Consequently, since the motive forces effective and 
applied ought to be in equilibrio, as well in virtue 
of their direct intensities, as in virtue of their mo- 
menta about the axis of rotation, we shall have, 
expressing by R and r the radii of the wheel and 
axle, the two following equations : 

P sin. e'^p sin. fl'-T-Q v^-^^4^, 

TR—fFr COS. e'-f (P+i>) cos. 0'= ^ k^ ^. 
Furthermore, as the velocity of the circumference 



FRICTION OF THE WAGGONS. 145 

of the wheel is equal to the velocity of translation of 
the centre, it follows that the velocity of rotation 
of a point situated at the distance 1 from the axis 
of the wheel will be to the velocity of translation in 
the ratio of 1 to R ; and, consequently, the same 
relation will exist between the accelerating forces, or 

^=R 

Substituting then this value in the second of the 
two equations above, and deducing the value of T, 
we obtain, firstly, 

T=/ P COS. e' . J +r (P+P) COS. «' • 4 +f • gl *• 

Supposing the planes but little inclined, we have 
very approximatively cos. 5" = 1. Besides, if we 
make 

/' p ^ +r (p+p) ^ =f(p+p). 

the expression of the quantity T will become 

Consequently, substituting this in the first equation, 
we derive in fine for the value of ^, 

*^7r^p — fc^(^^^-''--^-pf7^^' 

^V+J' R^ 

As the weights P and p are known, as well as the 
force Q, which expresses the resistance of the air, 

L 



146 CHAPTER V. 

at the unit of velocity ; as, besides, the momentum 

inertiae - k^ ib determined d priori, and as all these 

quantities are constant, we may, in order to sim- 
plify, make 

Q , 9 9 

— J— = a ana "^ j^ = -z — : — =: g . 

+ P ^ 1 4_ P _*: l+« ^ 

Then the accelerating force to which the motion of 
translation of the system is subjected, will be de- 
finitively 

4^ = g' (sin. 0'-f-qv^; 
and the motion of translation of the moving body 
may be considered as produced in spabe, by virtue 
of that force alone. 

The foregoing gives then the solution of the first 
portion of the problem, namely, the determination 
of the accelerating force. It now remains to deduce 
from the knowledge of the accelerating force, the 
velocity communicated to the mass by its descent 
on the first plane, and the distance to which it will 
be driven on the second plane by virtue of that 
velocity. In order to effect this, we will first con- 
sider the motion on the first plane. 

Let X be the distance traversed on the plane, 
when the body has acquired the velocity v; the 
quantity (f> being the accelerating force of the mo- 
tion, and that accelerating force being equally ex- 

V dv* 
pressed in general by the expression ""j"* we have 



FRICTION OF THE WAGGONS. 147 

V dv 

or making for a moment, sin. 6' —f'=^ h\ 

V dv 

This will be then the equation of the motion. In- 
tegrating it, and observing that the velocity is null 
at the point of starting, or that a?=o gives v'=^o^ it 
will be replaced by the following, 

2«-^ = log. wh' ■• 

or, expressing by c = 2* 7 1828 18, the base of the 
Neperian logarithms, it will be 

y 

which gives 

fills'* — 1 

qv'= b -jjp: 



c«^«^' = 



e"" * 



This relation then makes known the velocity ac- 
quired by the body after it has traversed the dis- 
tance X on the first plane. 

It will be recognised therein that the greater x is, 
the greater also becomes v ; and for x=oo we have 
qv^=b' or ff>=o; that is to say, the motion, as it 
continues, approaches more and more to uniformity. 
But it will be remarked that, since the value of qv^ 
may be written under the form 

qv^=V (1 "^iS^)' 



148 CHAPTER V. 

the motion will be sensibly uniform as soon as x 
becomes large enough to make the fraction of the 
second member inconsiderable with reference to 1 ; 
and as or is here an exponent, it is plain that this 
condition will quickly be fulfilled. From this point, 
then, we shall have 

and the motion will no longer differ from uniformity 
but by an inconsiderable quantity. This in fact, as 
experience proves, does really take place within a 
very short time. 

The preceding inquiry gives then the velocity at 
any point whatever of the first plane ; and if we 
call /' the length of the plane, and V the velocity of 
the body the moment it arrives at the bottom of the 
plane, we see from the equation just obtained, that 
this velocity will be 

which solves the second part of the problem. 

Now that we have the velocity of the moving body 
at the foot of the first plane, and consequently at the 
beginning of the second, since they are supposed to 
be united by a continued curve, the question is to 
determine at what point of the second plane the 
body will stop, which will lead us to the definitive 
solution of the problem. 

To this effect must be considered the motion of 
the body on the second plane. Calling 0'' the angle 



FRICTION OF THE WAGGONS. 149 

it forms with the horizon, as all the circumstances 
of the motion remain the same as before, except 
only that the inclination of the plane is less, we 
shall have by analogy 

—^ = 9 (sin. ^f-qv^). 

And as we have supposed that on the second plane 
gravity is less than friction, that is to say, we have 
sin. 0''<f, we will here make 

sin. r-./=-.r. 

Then the accelerating, or rather retarding force, 
since it is negative, of this second motion, will be 
expressed by 

V dv , 

Integrating this equation then, and observing that at 
the beginning of the plane the velocity is V, or, in 
other words, that 07 = gives i; = V, it will be re- 
placed by the following, which is suitable to every 
point of the motion. 






(Consequently, if V stand for the distance traversed 
by the body on the second plane, at the moment 
when its velocity becomes null, this equation will 
still subsist if we make in it at once 

, 1; = 0. 

Thus it will become 



150 CHAPTER V. 



2 qgr = log. 



V'+qV 



or 



^ — 1 + -yT > 

and putting for gV^ its value concluded from the 
motion on the first plane, this equation will become 

6' e**^'" — 1 

!L I 1 ^jjf'i' 

If' — e^9ti' _ 1 « 

Finally, if instead of g\ b' and b'\ their values be 
restored, and if, moreover, h' stand for the vertical 
height which the body has descended on the first 
plane, and h'' the vertical height which it has de- 
scended on the second, which gives 

Y and sm. 5 = -w? 



sin. 5'= -v" and sin. 5''= -v/ > 



the relation just obtained above will become 

K-fV _ r_ e"^' -1 ?^ 

•^ e*^' — 1 

This is the definitive relation between the co-ordi- 
nates of the points of departure and arrival of the 
moving body, the various data of the problem and 
the friction sought. 

When in this equation we suppose 9=0, the 

second member reduces itself at first to -, but 



FRICTION OF THB WAGGONS. 151 



it changes to 









and dividing by y — 1 , it becomes 

r_ y^--»+y--^» + y---» +1 

r r 

which for 5=0 or y= 1 , reduces itself to 7?/ Xp = 1 . 

Wherefore in this case, that is to say if the motion 
took place in a vacuum, the above relation would 
become 

/r-r^^^ whence /—^rpyr- 

Consequently, we should then have the friction re- 
quired, by dividing the sum of the vertical heights 
which the body has descended, by the sum of the 
spaces it has traversed; and it will be remarked 
that in this case, since there would be no resistance 
of the air, the motion of the body on the first plane 
could never attain uniformity. 

We have seen what the general relation becomes, 
on supposing f =0 ; if moreover we make/=o, that 
relation reduces itself to 

A' + r = o or r=-h'. 

Consequently were there neither friction nor re- 
sistance of the air, the moving body would rise 
on the second plane, supposing it inclined contrari- 



152 CHAPTER V. 

wise to the first, to a height equal to that from 
which it has descended ; and we quote these results 
because, being easily deduced from the direct ex- 
amination of each supposition, they serve here to 
verify the calculation. 
To return to the general formula, making in it 

*— 7" "TUP ^ 

^ cJ^i - 1 
we perceive that it may be written under the form 

ft-K'- ^ ' 
whence is derived for the value of the friction /, 

•^-r+rY * 

Thus, when, after having submitted a body of a de- 
termined weight, to the above experiment, on two 
planes of known inclination, the quantities K X h" 
and r shall have been found, it will suffice to cal- 
culate the corresponding value of Y, and introducing 
it with the other data in the expression of/, we may 
deduce the value of this latter quantity, which will 
be the friction sought. 

This method has the advantage of not depending 
on the execution more or less imperfect of an in- 
strument, and of being applicable to considerable 
trains of waggons, as we shall presently apply it. 



FRICTION OF THK WAGGONS. 153 



Sect. IV. Experiments on the friction of waggons. 

According to this principle, experiments were 
undertaken on one of the inclined planes of the 
Liverpool and Manchester Railway in the following 
manner. 

From a point taken on the Sutton inclined plane, 
at 50 chains or 3300 feet from the base of that 
plane, were measured 34 distances of 10 chains or 
330 feet each. At each of these points was set 
up a staff numbered, and its level accurately taken. 
The following are the admeasurements of the level- 
ling, expressed in feet and decimals of feet. 

The staves have since been replaced by perma- 
nent posts, which are distinguished, by red marks, 
from those which serve to indicate the miles of the 
road. 



154 



CHAPTER V. 





Total difltance 






Nnnibcn of 


from the Itt 


Total fall below the Ist post, in feet 




the posts. 


post, in feet. 


and decimals of feet. 






feet. 


feet. Point of Btarting. 















1 


330 


3-47 




2 


660 


707 




3 


990 


10-62 




4 


1320 


14-36 




5 


1650 


1817 




6 


1980 


21-77 




7 


2310 


25-53 




8 


2640 


28-98 




9 


2970 


32-07 r Foot of the inclined 




10 


3300 


34*61 < plane, or rather mid- 




11 


3630 


35-06 [die of the curve. 




12 


3960 


35-19 




13 


4290 


35-23 




14 


4620 


35-37 




15 


4950 


35-71 




16 


5280 


36-17 




17 


5610 


36-44 




18 


5940 


36-66 




19 


6270 


36^80 




20 


6600 


36*92 




21 


6930 


37-06 




22 


7260 


37-14 




23 


7590 


37*22 




24 


7920 


37-37 




25 


8250 


37-34 




26 


8580 


37-63 




27 


8910 


3792 




28 


9240 


38-14 




29 


9570 


38*35 




30 


9900 


38*54 




31 


10230 


38*67 




32 


10560 


38*77 




33 


10890 


38*92 




34 


11220 


39-08 





On the ground where these experiments were 
made, a little beyond the foot of the inclined plane, 



FRICTION OF THE WAGGONS. 155 

the waggons had to cross three junction roads, each 
of which required the passing over three switches. 
This made in all nine switches, either on one side 
of the rails or on the other. On passing over each 
of these obstacles, the waggons received a jolt from 
the unevenness of the road, and must have been 
retarded in their progress. The ground, therefore, 
is not favourable to the experiments, and tends to 
include in the friction the inevitable imperfections 
of the road. 

The waggons employed in the experiments are 
of the following construction. They consist of a 
single platform supported on four springs; the 
wheels are 3 feet in diameter, and are fixed to the 
axle-tree, which turns with them ; the body of the 
carriage rests upon the axle-trees, but outside of 
the wheels ; that is to say, that the axles are pro- 
longed through the nave in order to support the 
carriage. At the bearing they are turned down to 
1} inches in diameter. By this disposition the 
body of the axle-tree preserves its usual strength to 
resist the shocks received by the wheels in the 
motion, and the bearing- may at the same time be 
reduced to the slender diameter of If inches, be- 
cause that part has nothing but the body of the 
waggon to sustain. The chair is armed with a 
piece of copper at its rubbing point on the axle, 
and the grease, placed in a small cast-iron box 
above the axle, runs on it slowly, but without in- 
terruption, during the whole of the motion. This 



156 CHAPTER V. 

grease-box, filled every morning, is sufficient for the 
need of the whole day. In the experiments no 
alteration whatever was made in these dispositions, 
every thing being left the same as it is in the daily 
work, both with regard to the waggons and to the 
rails. Among the waggons there are some, the 
axle-bearings of which, instead of being from one 
end to the other of a uniform diameter of If 
inches, are thickened near the frame of the carriage 
by f inch, and are, on the contrary, diminished as 
much at the other end. The axle-bearing thus 
consists of three cylindrical parts equal in length, 
and the diameters of which are 2^, If, and If 
inches. 

The object of this disposition is to leave the 
mean diameter of the axle-bearing the same as 
before, but to transfer, however, the greatest force 
to the point which seems to suffer the most. These 
axles, few in number, are but an essay of which 
experience has not yet confirmed the advantage. 

As all the experiments we are about to report 
have been made in a manner perfectly similar, we 
shall give the details merely of one of them, and 
shall afterwards collect in a Table the results which 
all have produced, with the elements of the calcu- 
lation for each of them. 

On the 1st of August, 1834, 24 loaded waggons 
taken indiscriminately, were conveyed to the ground 
of the experiments by the engine Atlas. The weight 
of the 24 waggons, taken accurately with their load, 



FRICTION OF THE WAGGONS. 157 

amounted to 104*50 tons, and that of the tender- 
carriage of the engine, which remained attached to 
the waggons, was 5*50 tons, forming altogether an 
assemblage of 25 carriages, weighing 110 tons. 

The middle carriage of the train being placed on 
the plane precisely opposite the starting point or 
post No. 0, and the engine being removed pre- 
viously, the brakes were taken off at once at a 
signal given, and the 25 waggons committed to 
gravity on the plane. They continued their motion 
to 108 feet beyond the post No. 32, having thus 
traversed on the first plane a distance of 3300 feet 
with a vertical fall of 34*61 feet, and on the second 
a distance of 7368 feet with a fall of 4*21 feet. In 
this experiment then we have : 

r=3300, V=34-61, r=7368, r=4-21. 

We have just seen, besides, that the weight of the 
train was 

P+l>= 110 t, or in lbs. P+p= 110 X 2240 lbs. 

It is also known that the quantity e, which ap- 
pears in the equations, and which expresses the 
base of the hyperbolic logarithms, has for its value 

^ = 2-71828; 

and that the gravity g, expressed in English feet 
per second, is 

g = 3S feet. 
Finally, the resistance of the air per square foot of 



158 CHAPTER V. 

surface, at the velocity of 1 foot per second, is 
expressed, as we have seen, for 6=1*05, by 

Q=00125; 

and the resisting surface of the train, measured as 
has been explained in the preceding chapter, viz., 
at 70 square feet for the transverse section of the 
train and 10 square feet per waggon, amounted in 
all to 320 square feet. 

Nothing remains then, in order to have all the 
elements of the calculation, but to determine the 
value of the quantity n, viz. 



k 



.9 



n = 



This determination is easy ; for p is the weight of 
aU the wheels with their axle-trees, or as many times 
'85 ton as there are carriages, and P+ j) is known. 
Moreover, considering the wheel as a full cylinder, 
in which the weight of the axle should compensate 
for the void existing between the spokes, we should 
have approximatively, from the theoretical deter- 
mination of momenta inertise, 

but some experiments made on axles separated from 
the carriage, with a view to determine precisely their 
centre of oscillation, having given for that fraction 
the number '54, we will adopt that value. We shall 
have then 



FRICTION OF THE WAGGONS. 159 

R2 — ^^ > 

and consequently the expression of the quantity n 
will here become 

^^ 25 X -85 
n = -54 X — jjQ — = 104. 

The'se various values being substituted in the ex- 
pression of Y, give 

Y= 1-7040; 
and consequently the friction is 

/= 002635 or 590 lbs. per ton. 

The calculations relative to the other experiments 
are performed in a maimer entirely similar. Only, 
in three of them, to wit, the experiments VIII. IX. 
and X., which, besides the waggons, included also 
an engine, the value of / was first found, as before, 
and the friction of the whole train was concluded 
from it. But it was not till after having subtracted 
the friction proper to the engine itself, in conse- 
quence of a special experiment made immediately 
before and on the same spot, that the remainder 
was divided by the weight of the train, exclusive 
of the engine ; and thus was obtained the friction 
per ton proper to the waggons. The special ex- 
periment here noticed, and from which we derive 
the friction proper to the engine, at the moment of 
the observation, wiD be reported further on. 

In the experiments V. and IX. .the train could 



160 CHAPTER V. 

not be made to start precisely from the post No. 0, 
and the vertical fall and distance traversed varied in 
consequence ; but account has been carefully taken 
of this in the calculation, as may be remarked in the 
Table. 

During all these experiments the weather was fine 
and calm, and, as has already been said, nothing 
had been changed in the ordinary state of the 
waggons or the rails. 



FRICTION OP THE WAGGONS. 



J 



jJlJ 

lllli 









I 
I 
j 

5 ? T" ?> f 9 "P * 



J'oSSSSSS 



||2?|f"| 



•11 






illll-fjnlltl 

lllliiiHiiiii 



Hi 






5S2S2 



I! 



timtii t i 



162 CHAPTER V. 

From these experiments, the mean friction of the 
waggons, taken independently of the resistance of 
the air, amounts to -g^ of the gross weight of the 
waggons, or to 5*76 fi^s. per ton; but to simplify 
the calculations, we will take it at 6 lbs. per ton, 
which makes s^-g of the weight of the waggons. 

These are the results which ought to be used, 
when, for the resistance of the air, the determina- 
tion deduced from the most recent and most exact 
experiments on the subject is used, and when ac- 
count is taken, as it ought to be, of the length of 
the prism formed by the train in motion, as well as 
of the effects of the air against the rotation of the 
wheels and the accessory parts of the waggons. 
But if the calculation were limited to the use of 
the determination of Borda, which does not enter 
into the consideration of the diminution of re- 
sistance of lengthened bodies, and if account were 
taken only, as is the custom, of the resistance of the 
air against - the front surface, or transverse section, 
of the train ; that is to say, if the calculation of the 
foregoing experiments were performed anew, with 
Borda's datum, and giving to S the value indicated 
by the waggon of greatest section, then it would be 
found that the friction of the waggons should be 
taken at 7 lbs. per ton. 

It appears then, from this result, that for the 
mean velocity of the trains during the experiments, 
it would be indifferent to compute the friction of 
the waggons at 5*76 lbs. per ton, taking account of 



FRICTION OF THE WAGGONS. 163 

the real resistance of the air and of its effects against 
the accessory parts noticed above, or to take the 
friction of the waggons at 7 9>s. per ton, accounting 
merely, according to Borda, for the resistance of the 
air against the waggon of greatest section. On the 
other hand, as, during the work of the engines, their 
velocity is so much the greater as the train they 
draw is less considerable, whence the resistance of 
the air increases as the friction of the train di- 
minishes, it will equally be found that either of 
the two preceding calculations leads to very nearly 
the same result, for the total resistance opposed by 
the moving train, and that it is only in cases of 
extreme velocity that the two modes of calculation 
present a notable difference. 

Without any important error then, the second 
of the two modes of calculation may be used. It 
IB that which we had indicated in a former work 
(Theory of the Steam Engine) , when unacquainted 
with any otiher researches on the resistance of the 
air than those of Borda ; but now that M. Thibault's 
experim^its have enabled us to employ a method 
much more exact, we have duly given it the pre- 
ference, remarking at the same time that the defini- 
tive results of the calculations will not thereby be 
notably changed. 

This satisfaction, however, attends the coincidence 
which we have just noted, viz., that an error in the 
valuation of one of the two elements of the total 



164 CHAPTER V. 

resistance of the trams, would cause no important 
error in the calculation of the effects of the engines. 



Sect. V. Of the causes of variation in the friction of 

carriages. 

In the preceding experiments we employed as 
much as possible trains composed of a great number 
of carriages, because there often exist great dif- 
ferences between the individual frictions of two 
waggons of similar construction, and that it is only 
by uniting them in numerous trains, that the com- 
pensation which establishes itself between their dif- 
ferent frictions can lead to a uniform mean result. 

We must add, moreover, that the determination 
of the friction, which we have just obtained, refers 
to the waggons whose construction has been indi- 
cated above, and to the state of the Manchester and 
Liverpool Railway. As, however, on other lines, 
different circumstances may occur, it becomes ne- 
cessary to notice here the variations which may 
result from them in the friction of the carriages. 

The causes of the variation of friction are of four 
kinds: 1. the construction, the maintaining, and 
greasing of the carriage ; 2. the state of the rails ; 
3. the diameter of the axle-bearing and that of the 
wheel; and, 4. the proportion between the total 
weight of the carriage and that of the body of the 
carriage taken separately. 



FRICTION OF THB WAGGONS. 165 

That the influence of these four causes may be 
quite clear, we will refer to what has been said in 
sect. III. of this chapter. It was there seen that 
the friction of a carriage consists of two parts: 
one owing to the friction of the axle, which de- 
pends only on the weight of the body of the 
carriage ; and the other owing to the rolling of the 
wheel on the rail, which depends on the total weight 
of the carriage. It has been seen that the first of 
these frictions produced against the motion a force 
which we have represented by 

and the second a force represented by 



/" (P+p) 1-. 



f denoting the coefficient of the friction of axles, 
/" that of the rolling friction, r the radius of the 
axle-bearing, and R that of the wheel. But in order 
to simplify, we have replaced the two expressions by 
a single one, making 

/T^+r(P+/>)^=/(P + p); 

that is to say, instead of entering into the consider- 
ation of these two separate frictions, we have been 
content to consider the single force resulting from 
their union, and which we have supposed propor- 
tional to the total weight (P+p) of the carriage. 



166 CHAPTER V. 

But it is now requisite to direct a moment's 
attention to this expression. 

Ist. Since the quantity/' expresses the friction of 
the axle on its chair, for a given weight of the body 
of the carriage, it is plain that the more carefully 
roimded, polished, and greased the axle is, and the 
more easily the metals in contact slide upon one 
another, the less the coefficient/' will be. On this 
first term, then, is felt the influence of the mode of 
construction and greasing of the carriage. 

2d. From the same motive, the influence of the 
state of the rails, and of the perfect roundness of the 
wheels is felt on the factor f'\ which expresses the 
coefficient of the rolling friction. 

3d. The smaller the diameter 2r of the axle-bear- 
ing, the. more the first term, or resistance due to the 
friction of the axle, will be diminished ; and simi- 
larly, the more the diameter 2R of the wheel shall be 
augmented, the more thereby will be diminished the 
two partial frictions which take place, either on the 
axle or on the raU. 

4th. Finally, between two carriages wherein all 
the preceding conditions were strictly identical, 
some difierence might yet arise in the value of the 
definitive friction / In efiect, the preceding re- 
lation giving 

_ , ^ ^ r „ \ 

f=fY^' R +/" R' 

it is visible that the invariability of the quantities/', 
f'\ r and R will not prevent a variation in the value 



FRICTION OF THK WAGGONS. 167 

of /, according to the magnitude of the fraction 

p 

-= , that is to say, according to the ratio be- 

F + p 

tween the weight of the body of the carriage and 

the total weight of the waggon. 

From these divers observations, it becomes clear 
that on the same railway, the definitive friction /, of 
which we have found above the mean value 6 fibs, 
per ton, may vary according to the state of the 
waggons, the state of the rails, and the proportion 
of the load to the weight of the carriage ; and that 
between carriages differently constructed, the fric- 
tion may vary yet again, according to the diameter 
of the axle-bearings and of the wheels. 

The preceding considerations show that the valu- 
ation of the friction, which we obtained above, ought 
to be imderstood only of carriages similar to those 
which were submitted to experiment, and subject to 
like conditions, viz. with iron axles, turning on 
brass chairs and provided with self-acting grease- 
boxes ; with three-feet wheels and axle-bearings 1 f 
inches ; with the use of a well-kept railway, and 
finally with the usual proportion of about ^ between 
the weight of the body of the loaded carriage and 
the total weight of the waggon. Were these condi- 
tions materially altered, a new determination of the 
friction would become necessary. 



CHAPTER VI. 

OF GRAVITY ON INCLINED PLANES. 

We have seen, in the preceding chapter, how the 
resistance caused on a railway by the friction of the 
waggons may be valued. But it sometimes happens 
that this friction is the smallest part of the total 
resistance which the engine has to overcome, in 
order to effect the motion of the train. This case 
occurs when the way is not level, and the train 
is obliged to ascend an acclivity. The resistance 
then caused is, as every one knows, much greater 
than on a level line, and in consequence it becomes 
necessary to take account of it in the calculations. 

When a body is placed on an inclined plane, the 
weight which urges it, and which always acts in a 
vertical line, is decomposed into two forces : one 
perpendicular to the plane, and which measures the 
pressure produced against the plane, by virtue of 
the weight of the moving body, and the other ^ 
parallel to the plane, and which tends to make the 
body slide or roll along the declivity. The latter 
force, which we will call the gravity along the plane, 
would inevitably drag the body towards the foot 
of the declivity, were it not counteracted by a con- 



GRAVITY ON INCLINED PLANES. 169 

trary force. When therefore a train of waggons has 
to ascend an inclined plane, the moving power must 
apply to it: firstly, a force able to overcome the 
friction of the waggons themselves; and again, an- 
other force able to overcome the gravity in the 
direction of the plane. If, on the contrary, the 
mover draw the train of waggons down the plane, 
then, in order to produce the motion, it will evi- 
dently have to apply only a force equal to the dif- 
ference between the friction proper to the waggons 
and the gravity, since the latter force then acts in 
the same direction as the mover. 

When a body of a given weight is set on a plane 
of a given incUnation, we know that, in order to 
obtain the gravity of the body along the plane, its 
weight is to be multiplied by the fraction which 
expresses practically the inclination of the plane. 
Thus, for instance, on a plane inclined ^, that is 
to say, on a plane which rises 1 foot on a length of 
89 feet measured along the acclivity, the gravity of 
1 ton, or 2240 lbs., is 

??^ = 25-2 lbs. 
89 

Moreover, when a train of waggons ascends an 
acclivity, the engine has not only to surmount the 
gravity of the waggons of the train, but Ukewise its 
own gravity and that of the tender which follows it ; 
and these forces do not present themselves when the 
motion takes place on a horizontal line. It is then 



170 CUAFTBR VI. 

on the total weight of the train, that is, including 
engine and tender, that the resistance caused by 
gravity on acclivities is to be calculated. 

If it be supposed, for instance, that a train of 40 
tons, tender included, be drawn up a plane inclined 
^, by an engine weighing 10 tons, it is clear that 
the definitive resistance opposed to the motion by 
the train wiU be 

40 X 6 fts. = 240fi^s., friction of the carriages 

at 6 lbs. per ton . . . 240fi^s. 

50 X ^9^ = 1 258 lbs. , gravity of the 50 tons 

of the train (reduced to 
lbs.) on a plane in- 
cUned^,tobeadded 1258 



Total resistance arising from friction and 

gravity 1498 fts. 

If, on the contrary, the same train had to descend 
a plane inclined fwb' ^^^ resistance it would then 
offer would be 

40 X 6 fi^s. =240 9>s., friction of the waggons 240 lbs. 
50xf^^=112fts.,gravity of the train, to 

be deducted 112 



Definitive resistance arising from friction 

and gravity 128 fts. 

In general, let M be the weight of the train, in 
tons gross and including the tender ; let m be the 



GRAVITY ON INCLINED PLANES. 171 

weight of the engine, expressed also in tons ; k the 
friction of the waggons per ton, expressed in 9>s., as 
has been explained in the preceding chapter; finally, 
let g be the gravity, in 9>8., of 1 ton on the plane in 
question. It is clear in the first place, firom what 
has been said above, that the quantity g will be 
equal to 2240, multiplied by the practical inclina- 
tion of the plane ; so that if - express that inclina- 
tion, or the ratio of the height of the plane to its 
length, we shall have, to determine ^, the equation 

2240 

This premised, the friction of the waggons will 
have for its value 

fcM. 

Again, since g expresses the gravity of 1 ton, it is 
plain that 

g (M + m) 

will represent, in lbs., the gravity of the total mass, 
train and engine, placed on the inclined plane. 

Thus, according as the motion takes place in 
ascending or in descending, the total resistance, 
in 9>s., offered by the train on the inclined plane, 

will be 

*M ± jf (M + m) = (fc ± jf) M ± jrm, 

an expression in which the sign + belongs to the 
ascending motion, and the sign — to the descending 
motion, of the train. 



172 



CHAPTER VI. 



It will always be easy then to obtain the number 
of lbs., which represents the resistance opposed by 
a train in motion on a plane of a given inclination. 
This is the only result which we want at this mo- 
ment ; but as the intervening of inclined planes on 
railways brings with it some particular considera- 
tions, we will return to this subject further on, in 
order to solve the various problems that may occur. 

We have said above that when a body is placed 
on an inclined plane, its weight is decomposed 
into two forces, one acting along the declivity, as 
has been explained, and the other acting normally 
to the plane, and measuring the pressure which the 
weight of the body produces on the plane. In this 
case then, the weight of the train, with reference to 
the sustaining plane, is now expressed only by the 
normal component just mentioned, and not by the 
total weight of the waggons. Consequently, to be 
thoroughly accurate, instead of then reckoning the 
friction of the waggons from their total weight, it 
ought to be reckoned only from the normal com- 
ponent on the plane. This force is to the weight of 
the waggons, as the horizontal length of the inclined 
plane is to its length measured along the declivity. 
But as there never occur, on railways, planes so 
much inclined as to render the difference between 
those two lines not wholly inconsiderable, it is per- 
fectly useless to make a distinction on that head. 

For instance, on a plane whose practical inclina- 
tion shall be y^, which is a steep ascent for a rail- 



GRAVITY ON INCLINED PLANES. 173 

way, we find by geometry that the horizontal length 
of the incUned plane will be to its length measured 
along the declivity, in the ratio of the numbers 

99995 
100000" 

The difference then between the absolute and the 
relative weights of the waggons, is always an inap- 
preciable quantity in practice. For this reason, in 
all cases, we shall reckon the friction of the waggons 
placed on inclined planes, at the same rate as if they 
were placed on a level line. 



CHAPTER VII. 

OF THE PRESSURE PRODUCED ON THE PISTON BY 
THE ACTION OF THE BLAST-PIPE. 

Sect. I. Of the effects of the Blast^pipe. 

Wb have just examined and measured successively 
several of the resistances which are opposed to the 
engine in its motion, viz., that of the waggons along 
the rails, and that of the air against the trains. 
But among other resistances which the piston has 
yet to overcome, is one arising from the disposition 
of the engine itself, and of which it will be proper 
to treat before proceeding further. 

The steam, after having exerted its action in the 
cylinder, might escape into the atmosphere by a 
large opening. It would then be possible for it 
entirely to dissipate itself in the air, during the 
time the piston takes to change its direction. Con- 
sequently the steam would in nowise impede the re- 
trograde motion of the piston, whatever might be the 
velocity of the piston. But the disposition adopted 
is contrary to this. The steam, on leaving the cy- 
linder, has no other issue towards the atmosphere 
than an aperture exceedingly narrow ; nor can it, 
by that aperture, escape totally within the time of 



PRESSURE IN THE BLAST-PIPE. 175 

one Btroke, except by assuming a very considerable 
velocity in its motion. For this, the steam in the 
cylinder must necessarily be at a pressure sensibly 
greater than that of the atmosphere into which it 
flows ; and as the pressure of the steam while flow- 
ing acts in all directions, and consequently against 
the piston, it results that the latter, instead of having 
simply to counteract the atmospheric pressure, finds 
an additional one to overcome, which is to be added 
to the divers resistances already measured. 

This new cause of resistance might, as has been 
said, b^ in a great measure suppressed, by enlarging 
sufficiently the outlet of the steam. But to do this 
would be to lose one of the most active causes of 
the definitive efiect of the engine ; for the object of 
the disposition of which we treat is to excite the fire 
sufficiently, and to produce, in a boiler oi small 
dimensions, the very great quantity of steam requi* 
site for the .rapid motion of the engine. To this 
end, the waste steam is conducted to the chimney, 
and thrown into it by intermittent jets, through a 
blast-pipe or contracted tube, placed in the centre 
of the chimney and directed upwards. The jet of 
steam, as it rushes with force from this aperture, 
rapidly expefe the gases which occupied the chim- 
ney. It, consequently, leaves behind it a vacuum ] 
and this is immediately filled by a mass of air rush- 
ing through the fire-grate into the space where the 
vacuum has been made. At every a^iration thus 
produced, the fuel contained in the fire-box grows 



176 CHAPTER VII. 

white with incandescence. The effect then is similar 
to that of a bellows continually urging the fire ; and 
the artificial current created in the fire-box by this 
means is of such efficacy for the vaporization, that 
were the blast-pipe suppressed, the engine would be- 
come almost useless, which proves that the current 
of air attributable to the ordinary draught of the 
chimney is in comparison but very trifling. 

We shall return in the sequel, when speaking of 
the vaporization of the engines, to the effects of the 
blast-pipe relative to the production of steam. At 
present we have only to consider its effects relative 
to the pressure it causes against the piston. 

For this purpose we must first examine how this 
pressure, necessary to the outflow of the steam, is 
produced in the cylinder. At that moment when 
the eduction-pipe opens, and the steam begins to 
escape into the atmosphere, its pressure is yet the 
same as it was immediately before, when it served 
as the motive force to produce the motion. The 
latter pressure then is that which takes place at the 
first moment, and which, by reason of its excess 
above the atmospheric pressure, produces the efflux 
of the steam. But as that pressure is very con- 
siderable, and as the gases acquire, as is well known, 
very great velocities, even under very weak motive 
or effective pressures, it follows that at this moment 
the steam necessarily rushes from the cylinder with 
an enormous velocity ; and as, moreover, its density 
is then very considerable, it results that the greater 



PRESSURE IN THE BLAST-PIPE. 177 

part of the steam escapes immediately, or at least in 
a very short space of time. However, as the efflux 
takes place, the pressure of the remaining steam 
diminishes, as well as its density. Consequently 
the issuing velocity of the steam and the quantity 
of it which flows out in a given time diminish at 
the same time. A point then occurs at which the 
spontaneous efflux of the steam by the blast-pipe 
no longer exceeds the velocity which, by reason of 
the size of the orifice, corresponds to the velocity 
of the piston in the cylinder. Beyond this point 
the issuing velocity of the steam cannot diminish, 
for the piston, continuing its stroke, forces it out 
of the cylinder as rapidly as itself performs its 
motion. It is then the velocity of the piston which 
fixes the lower limit of the velocity of efflux of the 
steam ; and consequently the smallest efiective pres- 
sure that can take place in the cylinder is that which 
is capable of producing, in the efflux of the steam 
by the blast-pipe, a velocity corresponding to that 
of the piston. 

Thus, at the moment of the opening of the educ- 
tion-pipe, there is a tendency to produce in the 
blast-pipe an effective pressure equal to that which 
the steam had during its motive action in the 
cylinder ; but the duration of this extreme pressure 
is in a manner instantaneous. It immediately 
diminishes rapidly, and soon attains its inferior 
limit, which afterwards subsists till the end of the 
stroke; and then is produced in the blast-pipe a 

N 



178 CHAPTER VII. 

uniform effective pressure, corresponding to a ve- 
locity of efflux of the steam measured by the velo- 
city of the piston. 

Again, as the two cylinders communicate with a 
single blast-pipe, it happens that each cylinder 
transmits to the blast-pipe alternately steam, first 
at a very high pressure, and then at a low one ; and 
these effects succeed each other in such sort, that 
when one cylinder supplies steam at a low pressure, 
the other on the contrary gives it at the higher pres- 
sure. As these alternations are exceedingly rapid, 
there must result in the blast-pipe a certain mean 
pressure, which forms in a manner a factitious 
atmosphere, in which the two pistons work. This 
factitious atmosphere it is necessary to know; for 
evidently as soon as it becomes known, it will 
suffice to substitute it, in the calculation, for the 
natural atmosphere, to take account, without any 
other difficulty, of the resistance exerted against 
the piston by the action of the blast-pipe. 

Before proceeding further, we will therefore ex- 
amine how this mean pressure existing in the blast- 
pipe, must be modified according to the different 
circumstances of the working of the engine. 

1st. If the velocity of the piston increases, without 
any other change being made in the engine, it is 
visible, from what has been said above, that the 
lower limit of the effective pressure in the blast- 
pipe will increase ; and according to the principles 
admitted in the flowing of fluids, it will increase 



PRESSURE IN THE BLAST-PIPE. 179 

nearly as the square of the velocity of the piston. 
But on the other hand, it will be seen further on, 
that with the same vaporization in the boiler, 
the velocity of the piston cannot increase, without 
the effective pressure in the cylinder diminishing 
nearly in the inverse ratio of that velocity. Hence, 
in the case before us, namely, that of an increase of 
velocity of the engine without an increase of vapo- 
rization, the inferior limit of the effective pressure in 
the blast-pipe will augment in proportion to the 
square of the velocity of the piston, and its superior 
limit will diminish in the inverse ratio of the same 
velocity. As we have seen besides, that the max- 
imum pressure in the blast-pipe is of a duration 
much less than the minimum pressure, it follows 
definitively that the mean effective pressure in the 
blast-pipe will receive an augmentation, simulta- 
neous and in a certain proportion with the velocity 
of the piston. 

2d. If, the velocity of the piston remaining the 
same, the vaporization of the boiler increase, it is 
plain that the velocity of the piston can then re- 
main constant, only because the steam arrives in 
the cylinder with a total pressure augmented nearly 
in the ratio of the vaporization, or with an effective 
pressure augmented in a manner corresponding to 
it. It is now therefore the superior limit of the 
effective pressure in the blast-pipe, which .will have 
an increase correspondent to the vaporization pro- 
duced, whereas the lower limit of the same pressure 



180 CHAPTER VII. 

being always indicated by the velocity of the piston, 
will on the contrary undergo no change. Thus, 
in this second case, the mean effective pressure 
in the blast-pipe must necessarily increase in a 
certain ratio with the vaporization of the boiler. 

3d. Finally, if the velocity of the piston remain 
the same, as well as the vaporization of the boiler, 
but if the orifice of the blast-pipe be diminished 
without altering the area of the cylinder, it is clear 
that the same velocity of the piston will then corre- 
spond to an issuing velocity of steam by so much the 
greater ; and that if, for instance, the area of the 
blast-pipe be reduced to the half of what it was 
before, the issuing velocity of the steam, corre- 
sponding to the velocity of the piston, will be 
doubled. But, from the principles of the efilux of 
fluids, this double velocity will require a motive 
or effective pressure nearly quadruple. Hence, in 
this case, the inferior limit of the effective pressure 
in the blast-pipe will vary nearly in the inverse ratio 
of the square of the orifice of efflux of the steam ; 
but the superior limit of the same pressure will not 
vary, since it is always fixed by the pressure of the 
steam during its action in the cylinder. Therefore, 
definitively in this third case, the mean efiective 
pressure in the blast-pipe will receive an aug- 
mentation increasing in a certain inverse proportion 
of the ori^ce of the blast-pipe. 

These divers effects would no doubt be susceptible 
of a solution more or less exact by calculation ; but 



PRESSURE IN THE BLAST-PIPE. 181 

considering their nicety and at the same time the 
imperfectness of the theory of the efflux of fluids, 
we deem it more useful for the applications, to 
endeavour to determine them in a direct manner 
and by observation. For this reason, we shall make 
use of the preceding considerations, only to guide us 
in the research of the laws which may be derived 
fit)m experience in this respect. 

We will nevertheless observe, that there is a 
moment when the pressure in the blast-pipe pro- 
duces no opposition against the motion of the 
piston. This effect depends on the circumstance 
that, from a disposition of the engine which we 
shall explain in speaking of the lead of the slide, 
the eduction-port of the steam is opened a little 
before the piston has reached the bottom of the 
cylinder. The result is, that during the short inter- 
val yet left for the piston to traverse to finish its 
stroke, the pressure in the blast-pipe is found acting 
in the direction of the motion, instead of acting 
against it. But as, nearly at the same moment and 
from the same disposition, the steam of the boiler 
comes in beforehand against the motion of the 
piston, it follows that the resistance owing to the 
blast-pipe is only replaced by a stronger resistance. 
As however the velocity of the piston is then nearly 
null, and as its action to produce the motion is 
equally without efficacy, we will admit that the one 
effect replaces the other, and shall enter on no 
distinction in that respect. 



182 CHAPTER VII. 



Sect. II. Experiments on the resistance produced 
against the piston by the action of the Blast-pipe. 

To measure the resistance produced against the 
piston by the action of the blast-pipe, and the modi- 
fications it undergoes according to the circumstances 
in which the engine works, we undertook a series 
of experiments, which we are about to describe. 

The blast-pipe of the engine Star being taken 
out of the chimney, the extremity of it was cut at 
the point where the cone was three inches in dia- 
meter, and the removed part was replaced by a 
bonnet conical at the bottom, and which was fitted 
at this point with screws on the remaining portion 
of the cone of the blast-pipe (fig. 36). At its upper 
part, this bonnet changed into a quadrangular con- 
duit aabb, each side of which was two inches and 
a half in width, measured in the inside. Of the 
four sides of this conduit, three were fixed, and 
perfectly smooth on their inner surface ; the fourth 
aa was moveable on a hinge c, and when pushed at 
aV, towards the inside of the passage, in which it 
moved with an easy friction, the steam-way became 
narrowed by so much. Thus, when this factitious 
blast-pipe was entirely open, it presented a square 
orifice whose side was 2*5 inches, that is to say, an 
area of 6*25 square inches ; and when the moveable 
side was forced into the opening 1^ inches, the 
efflux orifice was no more than 2*5 inches by 1 



PRESSURE IN THE BLAST-PIPE. 183 

inch, that is to say, was reduced to 2'5 square 
inches of area. By this means, then, the orifice of 
the blast-pipe could be altered at pleasure. 

In order to execute this change easily, without 
opening the chimney or stopping the engine, a rod 
M'O, fixed on the moveable side of the blast-pipe, 
communicated, by means of a lever MOQ, whose 
fixed point was at Q, with a long rod Mm, whose 
other extremity m reached to the engine-man's stand. 
This rod Mm was composed of two parts : one, 
ME, terminated by a nut E invariably fixed to the 
rod; and the other, me, terminated, on the con- 
trary, by screw-bolts which inserted themselves 
into the nut, and thus united the two pieces into 
one. The part me of this rod passed into a fork 
PN, where it was maintained by two collars, to 
prevent its sliding longitudinally. It then ter- 
minated by a crank handle T. When a certain 
number of turns were made with this handle, it 
is plain that the screw e was made to penetrate 
more or less into the nut E, and that, consequently, 
the rod mM was shortened or lengthened. Thus, 
as the point N was fixed, it is evident that the 
moveable side of the blast-pipe was by so much 
either drawn in or pushed out. 

To measure precisely these shortenings or length- 
enings of the rod, a fixed index i was attached to 
the steam-dome of the boiler, and the upper surface 
of the nut E was marked with divisions. When 
therefore, by the motion of the handle, the nut 



184 CHAPTER VII. 

approached the fork N, its divisions passed suc- 
cessively under the fixed index ; and consequently 
the addition to the length of the rod might be 
read immediately. The dimensions of the divers 
pieces were such, that this increase of length in* 
dicated precisely the contraction that had taken 
place in the blast-pipe. 

In order to obtain the pressure of the steam after 
it had left the cyUnder, a brass tube of half an inch 
in diameter, inserted into the pipe leading to the 
blast-pipe, brought a portion of that steam into a 
receiver, placed on the engine-man's stand. This 
tube, on leaving the compartment of the chimney, 
was protected against the effects of the external 
refrigeration of the air, by a thick covering of hemp 
carefully put on and defended by a coat of paint. 
The receiver into which the steam was conducted 
was 1 2 inches high and 3 inches in diameter. It bore 
three instruments adapted to measure the pressure, 
viz., an air-gauge, a thermometer, and a little 
syphon-manometer. The syphon-manometer had 
the inconvenience of filling with water, and was in 
consequence abandoned ; but during all the obser- 
vations which were made with the three instruments 
their indications accorded exactly. Only, after the 
stoppages of the engine, the thermometer-gauge was 
much longer than the other two in marking the 
pressure. 

The whole of this apparatus is seen represented 
in fig. 24 (PL V). VV is the tuhe which brings 



PRESSURE IN THE BLAST-PIPE. 185 

the steam from the blast-pipe to the receiver; A 
is the receiver, closed at its upper part by a safety- 
valve maintained in its place by the pressure of an 
ordinary spring-balance F ; B is the air-gauge, and 
r is the cock by which the steam arrived from the 
interior of the receiver to the ball of the instrument. 
C is the thermometer or thermometer-gauge ; dd is 
the tube which conducted the steam from the re- 
ceiver to the little syphon-manometer, which could 
not be figured for want of room. In fine, the dis- 
charging cock R, seen at the bottom of the receiver, 
served to let out the water which formed therein by 
condensation at the commencement of the experi- 
ments and till the mass of the system had acquired 
a proper temperature. The apparatus once suffici- 
ently heated, this cock, when opened, let out no- 
thing but a jet of perfectly transpareilt steam, and 
never any water, which proved that no condensa- 
tion of steam was taking place in the receiver. 

The steam was taken at the point where the pipes 
proceeding from each cylinder unite to form the 
origin of the blast-pipe. At tins point the pressure 
was successively that of the two cylinders. . Conse- 
quently the rapidity of the alternations of the pistons 
maintained there a mean constant pressure, at least 
as long as no variation occurred in the circum- 
stances which we shall presently speak of At the 
moment of the starting of the engine, when the 
velocity was but 2 or 3 miles per hour, the mercury, 
at every stroke of the piston, was seen to rise sud- 



186 CHAPTER VII. 

denly, in the air*gauge and in the syphon-mano- 
meter, to a height corresponding to about lfl>. of 
effective pressure per square inch. But this effect 
was produced and destroyed instantaneously, so that 
in the duration of one stroke, the space of time 
wherein the pressure was null was greater than that 
in which it was lib. above the atmospheric pres- 
sure. Afterwards, as the velocity of the eneine 
increased, the mercury rose permanenUy in the 
manometers, and its oscillations of level became 
less and less sensible. At the velocity of 16 to 18 
miles an hour a very sUght motion was still dis- 
cernible in the surface of the mercury at every 
stroke of the piston; but beyond that point the 
oscillations became insensible, and the pressure 
was no longer seen to vary but with the circum- 
stances which formed the object of the experi- 
ments. 

The apparatus being fixed on the engine, when, 
during the motion, the orifice of the blast-pipe was 
contracted, it immediately caused the pressure to 
rise in the manometers several pounds, according 
to the contraction made in the aperture, and on 
bringing back the blast-pipe to its former dimen- 
sions the pressure returned to the same point as 
before. Similarly, as the velocity of the engine 
increased or diminished, the pressure in the blast- 
pipe was seen to vary in a corresponding manner. 
And finally, whenever, by putting coke on the fire 
or water in the boiler, the vaporization of the boiler 



PRESSURE IN THE BLAST-PIPE. 187 

was temporarily diminished, the pressure in the 
blast-pipe was instantly seen to lower, and to re- 
sume its former degree only when the vaporization 
had resumed its ordinary activity. There remained 
no doubt then that the velocity of the engine, the 
rate of vaporization, and the orifice of efflux of the 
steam, had an immediate effect on the pressure in 
the blast-pipe. As to the pressure in the boiler, 
since the steam, before arriving at the blast-pipe, 
passed first through the cylinder, it is clear that 
the pressure in the boiler could not have modified 
the pressure in the blast-pipe, but by first modi- 
fying that of the cylinder. Now we shall here- 
after show that this latter effect, from the boiler 
to the cylinder, does not exist ; neither then could 
it exist fix>m the boiler to the blast-pipe. And, in 
fact, we observed that the augmentation of pressure 
in the boiler was, according to the circumstances, 
attended at times with an elevation, at other times 
with a diminution of pressure in the blast-pipe, as 
may besides have been remarked already in the 
experiments related in Section vi. Chapter II. 

Of the three circumstances just mentioned, as 
modifying the effects of the blast-pipe, the first that 
we chose to submit to inquiry was the influence of 
the velocity of the engine on the pressure due to the 
blast-pipe. For this purpose, the fire being kept in 
the same state of intensity, and the boiler regularly 
fed with water, in order to preserve, as much as 
possible, a uniform vaporization, and the orifice of 



188 CUAPTEB VII. 

the blast-pipe being maintained constant, we made 
the observations related in the following Table. We 
thereto add the last column, in which is inscribed 
the pressure which should have been observed, had 
the variation taken place exactly in proportion to 
the velocity. 

To perform this calculation, we take as our point 
of departure, in each series of experiments, the pres- 
sure corresponding to the mean velocity of the 
motion. 

We must, however, add here, that nothing is 
more difficult to obtain than uniformity in the va- 
porization of the engine. Every time that coke is 
thrown into the fire-box or water sent to the boiler, 
the production of steam is immediately reduced, 
though the velocity of the engine does not detect 
the change, on account of its acquired impulse ; but 
the difierence of vaporization is felt immediately in 
the receiver, where, as has been said, the manome- 
ters are seen to lower all at once and not to resume 
their usual degree till after a certain time. A con- 
trary effect takes place when the supply of the fire 
and feeding of the boiler are momentarily suspended, 
which especially happens during ascents, because the 
engine-men are then apprehensive of diminishing the 
power of the engine too much. These circumstances 
oblige us, as the Table shows, to recur to the mean 
of the observations, in order to obtain the corre- 
sponding pressures and velocities. 

We must equally give notice that in the two 



PRESSURE IN THE BLAST-PIPE. 



189 



series of experiments contained in the Table, the 
orifice of the blast-pipe was not the same. 



Experiments to determine the inflttence of the velocity of 
the motion, on thepresstare due to tJte blast-pipe. 





Observed effec- 






Effective pres- 
sure calcu- 


Velocity of 

the engine in 

miles per 

hour. 


tive pressure, on 
the opposite face 
of the piston, in 
lbs. per sq. inch. 


Mean 
velocity. 


Mean effective 
pressure, by 
observation. 


lated, in the 
direct ratio of 

the velocity 
of the motion. 


15- 
15-24 


4- 1 
4-4 / 


1512 


4-2 


4-3 


16-56 


4-9 


16-55 


4-9 


4-7 


16-95 
17-21 


4-3 1 
5-6 / 


17-08 


4-9 


4-8 


7-28 


1-8 


6-26 


1-8 


2-2 


9-11 


2-8 


8-57 


2-8 


2-8 


14-53 


4-4 


14-53 


4-4 


4-5 


16-39 


5-3 1 








16-67 


5-8 > 


16-67 


6-3 


6-2 


16-96 


4-8 , 








17-50 
17-73 


5-1 1 
6-2 / 


17-61 


5-6 


5-5 



We see by these results, that the eflFective pres- 
sure exerted against the piston, by the action of the 
blast-pipe, varies very nearly in the direct ratio of 
the velocity of the piston, or of the engine. 

From the considerations which we have presented 
above, it still remained to seek according to what 
law the pressure on the piston, in the action of the 
blast-pipe, varies with the ratio of the vaporization 
in the boiler, to the area of the blast-pipe through 
which the steam is forced to flow. With this view 



190 CHAPTER VII. 

were undertaken the experiments which we shall 
presently offer, note being carefully taken in them, 
of the velocity of the engine, of the area of the blast- 
pipe, and finally of the vaporization of the boiler. 

After having compared the observations among 
themselves, we find that the law to which they 
approach nearest is that of a simple proportionality 

to the ratio — , in which S' represents the total 



vaporization or the expenditure of water of the 
boiler, such as we observed it in the experiments, 
and represents the area of the orifice of the blast- 
pipe. It is for this reason that we annex to the 
Table of the experiments, a last column containing 
the resistance against the piston created by the 
blast-pipe, such as calculation would give it, sup- 
posing that it were directly proportional to the 
velocity of the engine, and to the ratio of the total 
vaporization to the area of the blast-pipe, that is to 
say, supposing it to be of the form 



To obtain the coefficient K, which should serve to 
operate this reduction, we first compared the pro- 
s' 
duct V — to each of the results given by observation, 

and thence deduced the value of K, which was 
found to be '0113. Consequently we calculate the 
last column bv the formula 



PRESSURE IN THE BLAST-PIPE. 191 

•0113 t;—. 



With regard to the observations of velocity and 
pressure inserted in the Table which we are about 
to present, we must notice that each of them is a 
mean taken on from ten to twenty consecutive ob- 
servations, which by so much the more insures their 
accuracy. Nevertheless, as these observations were 
all made at the same period of the experiment, and 
at very short intervals of time from each other, it is 
still found, on looking over the results to discover 
the law which represents them, that the difficulty 
already mentioned, of maintaining the imiformity of 
the vaporization in the boiler, occasions from time 
to time anomalies not inconsiderable in the observa- 
tions. But on recurring to a mean taken between 
observations made at two different periods of the 
experiments, those anomalies are found to disappear 
almost entirely ; which is a proof that they arise 
solely from this, that the observed pressure in the 
blast-pipe results from the momentary vaporization 
of the engine, animated or slackened during that 
portion of the experiment, whereas the calculated 
pressure can be grounded only on the mean vapori- 
zation of the whole experiment. 

The observations we have just made are relative 
to the last two columns of the Table. In that which 
contains the dimensions of the blast-pipe, instead of 
giving those dimensions in square inches, as re- 
sulted from the form of the blast-pipe employed, 



192 CHAPTER VII. 

we give the diameter of a round blast-pipe offering 
the same area of orifice. As the circular form is 
the only one in use, we thought that the Table pre- 
sented in this manner, would become more commo- 
dious for practical appUcations. 

Finally, we must yet add, that in the experiments 
about to be related, we have sometimes reduced the 
area of the orifice of the blast-pipe to but 2*50 and 
3*125 square inches, and thence resulted, even for 
very moderate velocities, very great resistances 
against the piston. But such contractions are not 
in use: before the variable orifice which we have 
described was fitted up on the Star engine, the 
blast-pipe was of the diameter of 2f inches, or 4*5 
square inches of area, which is a measure usual 
enough in these engines. The blast-pipe then, in 
the regular use of it, produces only resistances 
proportioned to that dimension; and this remark 
is necessary, that the results related in the Table 
may not be r^i^rded as mean data suitable to the 
regular work of locomotives. 



\ 



PRESSURE IN THE BLAST-PIPE. 



193 



Experiments on the resistance produced against the piston by 

the action of the blast-pipe. 





Vapatintion 






Effeetire pres- 


EfliBCtiTe pras- 




daring the 






rareagamat 


sure, ealca- 




Bxperiment, in 




Velodtjrof 


the piston, 


latedbythe 


Dtte of the experiment, ead 


cubic feet (tf 


Diameter 


theensine, 
innulea 


obeerred du- 


fonnuhi 


dedgnetmi of the eneine 
and its loed, tender indnded. 


water per 


of the 


ring the 
experiment. 


8' 

• Jftl ft 4k .a* ^^ 


hour. 


bbMt-pipe. 


per hoar. 


0113 _. 

e 


1836. 


cuhic feet 


inches. 


miles. 


lbs.persq.in. 


tbs.persq.in. 


Aug. 9, Star, from LiTer- 












pool to Manchester, with 












120*27 tons . . . . 


67-71 


1-995 


16-95 


4-3 


4-1 








15-00 
15-00 


5-01 . 
3-0 J* 


3-6/ * 








17-21 


5-6 


4-2 








15-24 


4-4 


3-7 


Aug. 9, Star, from Man- 






16-55 


4*9 


4*0 


chester to Liverpool, 












with 75-05 font . . 


68-79 


1-995 


16-96 


4*8 


4*2 






* 


17-50 


5-1 


4-3 








14-53 


4-4 


3-6 








16-67 


5-8 


4-1 








16-39 


5-3 


4-1 








17-73 


6-2 


4-4 


Aug. 9, 5'/ar,with 38*58 «»•. 


68-79 


1-995 


911 


2-8 


2-3 


Aug. 9, 5/flr,with 4 1 -9 7 «". 


68-79 


1-995 


7-28 


1-8 


1-8 


Aiig.9,Slfar, from liverp*. 












to Manch'. with 96*30 *». 


60-64 


2-821 


22-85 


3-0 


2*4 






* 


20-00 


2-4 


2-1 








20-00 


2-3 


2-1 








21-82 


1-8 


2-3 








17-56 


2-3 


1-9 


Aug. 10, Star, from Li- 






19-25 


2-0 


21 


verpool to Manchester, 












with 43-65 tons . . . 


65-49 


2-360 


23-64 
2000 


2-4 r® 


4-01 
3-4, 


3-7 








26-67 
25-00 


*'^l3-7 
1-8/^^ 


4-51 
4-2 


4-3 








20-69 


2-9 


3-5 


Aug. 13, Star, from Li- 






20-77 


2-2 


3-5 


verpool to Manchester, 












with 109-68 tons . . 


54-20 


2-360 


19-57 


1-0 


2-7 






1-995 


13*33 


2-4 


2-6 








1714 


3-8 


3-4 








10-29 


2-1 


2-0 








12-63 


1-6 


2-5 


Aug. 13, Star, from Man- 






12-47 


1-2 


2-5 


chester to Liverpool, 












with 48-48 tons . . 


62-83 


1-784 


21-82 


5-4 


6-2 








23-53 


5-0 


6-7 








18-75 


4-2 


5-3 








19-20 


3-4 


5-5 








2000 


\IV^ 


5-7 








2000 


5-7 



194 CHAPTER VII. 

Comparing the last column and the last but one 
of this Table, we recognise between them a suffi- 
cient coincidence for practical purposes. Conse- 
quently, in all cases wherein the resistance caused 
against the piston by the action of the blast-pipe 
shall not have been directly observed, it may be 
determined by the formula 

•0113 v—; 



in which v is the velocity of the engine in miles per 
hour ; S' the total vaporization of the boiler in cubic 
feet of water per hour ; o the area of the orifice of 
the blast-pipe expressed in square inches ; and the 
result of the calculation will give the pressure in the 
blast-pipe expressed in pounds per square inch. 
The pressure per square foot will be 144 times as 
much. 

With respect to the quantity represented here by 
S^ the experiment from which we deduced the 
formula shows, that the vaporization signified is 
the total vaporization effected in the boiler, that 
is to say, the vaporization counted before deduction 
of the water carried away in a liquid state with the 
steam. But as the engine Star makes habitually 
no waste of steam by the safety-valves, it is un- 
derstood that in engines in which this loss does 
take place, it is not considered as included in the 
value of S', and consequently, if a very nice accu- 
racy be desired, it will be proper, first of all, to 



PRESSURE IN THE BLAST-PIPE. 195 

subtract it from the vaporization effected, in order 
to obtain the quantity here expressed by S^ 
Making in the preceding formula 

•0113— = /, 

the pressure in the blast-pipe may be represented by 
the expression 

p V, 

in which p^ will be the ratio of the vaporization to 

the orifice of the blast-pipe, multiplied by a constant 

coefficient. 

Now, for engines which vaporize as much as 60 

cubic feet of water per hour, practice has established 

the use of a blast-pipe of 2*25 inches diameter, or 

3*96 square inches of area, which gives for the value 

S' 
of the ratio — , 



= 15-2 



396 

In constructing engines of a greater vaporizing 
power, it would be natural to increase the area of 
the blast-pipe in proportion to the quantity of steam 
to which it is to give issue. There is room therefore 
to think that the proportion thus established be- 
tween the production of steam and the area of the 
blast-pipe, will not be notably changed by the dif- 

ferent engine-makers. Consequently the ratio — 

may be regarded approximatively as a constant 
quantity, given by the above proportion. 



196 CHAPTER VII. 

Then the preceding formula will be reduced 
simply to the expression 

•175 r, 

which will be useful especially in valuing the pres- 
sure due to the blast-pipe in engines whose vapo- 
rization is unknown. In this formula, t; is the 
velocity of the engine, in miles per hour, and the 
result is the pressure in the blast-pipe, expressed in 
pounds per square inch. As the pressure per square 
foot is 144 times as much, it follows that if we 
require the pressure expressed in that manner, as 
will be found necessary in the course of this work, 
we shall obtain its value by the formula 

25-2 v. 

We shall then represent generally the pressure in 
the blast-pipe under the form 

and for the most ordinary cases, it will suffice to 
give to f\ in this expression, one of the constant 
values above mentioned, according to the measures 
employed. But if the engine in question should 
differ too considerably from the proportions which 
we have just indicated with reference to the area of 
the blast-pipe, it would be necessary to substitute 
for that approximate value of j?^ its value function 
of S' and o. 

In fine, to dispense with all calculation on this 
head, we here subjoin a Table, in which will be 
found, on inspection, the pressures in the blast-pipe 



T 



PRESSURE IN THE BLAST-PIPE. 197 

for given circumstances, and we continue that Table 
beyond the actual effects of locomotive engines. It 
will there be recognised how, by augmenting the 
orifice of the blast-pipe, the resistance against the 
piston, arising from that cause, may be diminished 
at pleasure ; and it may probably be found, in con- 
sequence, that in the regular work of locomotives, it 
might be useful to adopt a blast-pipe with a variable 
orifice, such as we employed temporarily in our 
experiments. Then, by contracting the orifice of 
efflux of the steam only just as much as is necessary, 
there will be no more resistance against the piston 
than what is indispensable for the proper action of 
the engine. 



I 



f 



198 



CHAPTER VII. 



Practical Table of the pressures against the piston, due to 

the action of the blast-pipe. 



Diame- 
ter of the 
blaat-pipe. 


VdocitT 

of the 

engine, 

in miles 

per hoar. 


EffiBcthe pcessure aninst the piston, in lbs. per square inch, the 
T^wnaatton of the Dotler, in cubic feet of water per hour, being: 


30 


40 


50 


60 


70 


80 


90 


100 


S inches. 


miles. 
6 
10 
15 
90 
S5 
SO 
85 
40 


Ifaa. 
0*5 
1-1 
1-6 

S'S 

S7 

3*9 
3-8 
48 


ft*. 

07 
1-4 
9-9 
99 
80 
4*3 
5*0 
5*8 


lbs. 
0*9 
1*8 
9*7 
30 
4-5 
5*4 
OS 
7-9 


lbs. 
ri 

9*9 
3*9 
4*8 
5*4 
0*5 
7-0 
8*0 


tbs. 

1*3 
9*5 
8*8 
5*0 
OS 
7*0 
8*8 
10*1 


tbs. 

t> 
»> 
>t 
>t 
If 
tt 


tbs. 

It 
II 
II 
11 
II 
»l 
II 
II 


lbs. 

f* 
II 
f> 
It 
It 
If 
tt 
It 


Siinchea. 


5 

10 
15 
SO 
S5 
SO 
35 
40 


0'4 
0-9 
1*3 

17 

9-1 
90 
3-0 
3*4 


00 

1-1 

17 
9*3 
9*8 
3*4 
4*0 
4*5 


07 

1*4 
9*1 
9*8 
3*0 
4*3 
50 
57 


0*9 
17 
9*0 
3*4 
4*3 
5'1 
0*0 
0*8 


1*0 
9*0 
8*0 
4*0 
5*0 
0*0 
7*0 
8*0 


1*1 

9*8 
3*4 
4*5 

0*8 
8*0 
9*1 


It 
II 
11 
II 
II 

II 
It 
II 


>l 
ft 
It 
•1 
It 
tt 
tl 
n 


Si inches. 


5 

10 

15 

90 

95 

SO 

35 

40 

45 

50 


0*3 

07 
10 

1-4 

17 
9-1 
9-4 
9*8 
8'1 
3-5 


0-5 

0-9 
1-4 
1-8 
9-3 
9*8 
3*9 

37 
4*1 
40 


0*0 
1*9 

17 
9*9 
9*9 
8*5 
4*0 
4*6 
5*9 
5*8 


07 
1*4 
9*1 
9*8 
3*5 
4*1 
4*8 
5*5 
0*9 
0*9 


0*8 
1*0 
9*4 
8*9 
4*0 
4-8 
5*0 
0*4 
7*3 

8*1 


0*9 
1*8 
9*8 
3*7 
40 
5*5 
0*4 
7*4 
8*3 
9-9 


ro 

9*1 
3*1 
4.1 
5*9 
0*9 

7*8 

8*3 

9*3 

10*4 


11 
tt 
tl 
•I 

1 :: 

It 
tl 
It 


9f inches. 


5 

10 

15 

90 

95 

80 

35 

40 

45 

50 


0*3 
0-0 
0*9 
VI 
1*4 

17 

9-0 
9-3 
90 
9*9 


0*4 
0-8 
1-1 
1*5 

1-9 
9*8 

9*7 
8*0 
3*4 
3*8 


0*5 
1*0 
1*4 
1-9 
9*4 
9*9 
8-3 
3*8 
4*3 
4*8 


00 
1*1 

17 
9*3 
9*9 
3*4 
4*0 
4*0 
5*1 
57 


07 
1*3 
9*0 

97 
8*3 
4*0 
4*7 
5*3 
0*0 

0*7 


0*8 
1*5 
9*8 
3*0 
3*8 
4*0 
6*8 
0*1 
0-8 
70 


0*9 
17 
9*0 
3*4 
4*3 
5*1 
0*0 
0*8 

77 
8*0 


10 
1-9 
9*9 

S-8 
4*8 

£•7 

0-7 
7*6 
8*0 

9-5 


3 inches. 


5 

10 
15 
SO 
95 
30 
85 
40 
45 
50 
55 
00 


0*9 
0*5 

07 
I'O 
1*9 
1-4 
17 
1-9 
9-9 
9-4 
9-0 
9-9 


0*8 
00 
1*0 
1*3 
10 

1-9 
9*9 
9*0 
9*9 
8*9 
3*5 
3*8 


0*4 
0*8 
1*9 
1*0 
9*0 
9*4 
9*8 
3*9 
3*0 
4*0 
4*4 
4*8 


0*5 
1*0 
1-4 

1-9 
9*4 

9*9 
3*4 
3*8 
4*8 
4*8 
5*3 
5*8 


O'O 
1*1 
17 

9*9 
9*8 
3*4 
3*9 
4*5 
5*0 
5*0 
0*9 

0*7 


O'O 

1*3 

1*9 
90 
3*9 
3*8 
4*5 
5*1 
5*8 
0*4 
7*0 
77 


07 

1*4 
9*9 

9*9 
3*0 
4*8 
5*0 
6*8 
0*5 
7*9 

7*9 

8*0 


0-8 
1*0 
9*4 
3-9 
4*0 
4-8 
50 
0*4 

7-9 

8*0 
8-8 
9*0 


3i inches. 


5 

10 
15 
90 
S5 
80 
85 
40 
46 
50 
55 
60 


0-9 
0*4 
0*0 
0*8 

ro 

1'9 
1-4 
l-fl 
1*8 
9*0 
9-9 
9-4 


0-3 
0*5 
0*8 
1*1 
1*4 
1*0 

1-9 
9*9 
9*4 

97 

8*0 
3*9 


0*3 
07 

1*0 
1*4 

17 
9*0 
9*4 

9*7 
3*1 
3*4 
3-7 
41 


0*4 
0*8 
1*9 
1*0 
9*1 
9*5 

9*9 
3*3 

37 
4*1 
4*5 
4*9 


0*5 
1*0 
1*4 

!•» 
9*4 
9*9 
3*3 
3-8 
4*3 
4*8 
5*9 
5*7 


0*5 
1*1 
1*0 
9*9 
9*7 
8*3 
3*8 
4*4 

4-9 

5-4 
6*0 
0*5 


0*0 
1*9 
1*8 
9*4 
8*1 

3*7 

4*8 

4*9 
5-5 
0*1 
0*7 1 

7*3 1 


07 
1*4 
9*0 
9*7 
3*4 
41 
4*8 
5-4 
0*1 
0*8 
7*5 
8*9 



I 

L 



PRESSUBE IN THE BLAST-PIPE. 



199 





Velocity 


EfliectiTe pressure aominst the piston, in tbs. per square inch, the 


Diameter 

of the 
blaat-pipe. 


of the 

engine, 

in miles 

per hoar. 


▼aporisabon of the boiler, 


in cubic feet of water per hour, be 


sing: 

100 


30 


40 


50 


60 


70 


80 


90 




mOes. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


34 Indies. 


6 


O'S 


0*9 


0*3 


0*4 


0*4 


0*5 


0*5 


0*6 




10 


0-4 


0-5 


0'6 


07 


0-8 


0*9 


VI 


1*9 




15 


0*5 


07 


0*9 


1*1 


1*9 


1*4 


1-6 


1*8 




90 


07 


0*9 


1-9 


1*4 


1*6 


1-9 


9*1 


9*3 




S5 


0*9 


1*9 


1*5 


1'8 


91 


9-4 


9-7 


9*9 




30 


I'l 


1-4 


17 


9*1 


9*5 


3*8 


3*9 


3*5 




35 


1-2 


1-6 


9-0 


9*5 


9*9 


3*3 


37 


4*1 




40 


1-4 


1-9 


S'3 


9*8 


3*3 


3*8 


4*9 


47 




45 


1-6 


9-1 


9-6 


3*9 


3'7 


4-9 


4*8 


5-3 




50 


1-8 


9-4 


9-9 


3*5 


4-1 


47 


5*3 


8*9 




55 


19 


9-6 


3-9 


8-9 


4*5 


5*9 


5*8 


6-5 




60 


9*1 


9-8 


3-5 


4-9 


4'9 


5-6 


6-4 


70 


3f inches. 


5 


0-2 


0'9 


0-3 


O'S 


0*4 


0*4 


0-5 


0*5 




10 


0-3 


0-4 


0-5 


0*6 


07 


0*8 


0*9 


1*0 




15 


0*5 


0*6 


0-8 


0-9 


ri 


1*9 


1*4 


1*5 




20 


0*6 


0*8 


ro 


1*9 


1-4 


1*6 


1*8 


9*0 




S5 


0*8 


I'O 


1-3 


1*5 


1*8 


9*1 


9*3 


9-6 




90 


O'Q 


1-9 


1*5 


1-8 


9*1 


9*5 


9*8 


3*1 




85 


l-l 


1-4 


1-8 


9*1 


9*5 


3*9 


3*9 


3*6 




40 


1*9 


1-6 


90 


9*5 


9-9 


3*3 


3*7 


41 




45 


14 


1-8 


9*3 


9*8 


3*9 


3-7 


4*1 


4-6 




50 


1*5 


9-1 


9*6 


3-1 


3-6 


4-1 


4*6 


5*1 




55 


17 


9'3 


9*8 


3-4 


3*9 


4*5 


6*1 


5*6 




60 


1'8 


9*5 


3*1 


37 


4*3 


4-9 


5*5 


6*1 


4 inches. 


5 


O'l 


0'9 


0-9 


0-3 


0*3 


0*4 


0*4 


0-5 




10 


O'S 


0*4 


0-5 


0*5 


0*6 


0-7 


0*8 


0*9 




15 


0-4 


0-5 


07 


0*8 


0*9 


I'l 


1*9 


1-4 




SO 


0-5 


07 


0-9 


1*1 


1-3 


1*4 


1*6 


1*8 




S5 


07 


0*9 


l-l 


1*4 


1*6 


1*8 


9*0 


9*3 




30 


0*8 


1-1 


1*4 


1-6 


1-9 


9-9 


9*4 


9*7 




35 


0*9 


1*3 


1-6 


1-9 


9-9 


9-5 


9*8 


3*2 




40 


1-1 


1*4 


1-8 


9-9 


9-5 


9-9 


3*9 


3*6 




45 


1*9 


1-6 


90 


9-4 


9*8 


3*9 


3-6 


4*1 




50 


1*4 


1-8 


9-3 


97 


3*9 


3*6 


4*1 


4-5 




55 


1-5 


90 


9'5 


3-0 


3*5 


4*0 


4-5 


50 




60 


1-6 


9*9 


97 


3*9 


3*8 


4'3 


4*9 


5-4 



CHAPTER VIII. 



OF THE FRICTION OF LOCOMOTIVE ENGINES. 



ARTICLE I. 

OF THB FRICTION OF UNLOADED LOCOMOTIVE 

ENGINES. 

Sect. I. Of the divers elements of the friction of 

locomotive engines. 

After having examined the resistance offered by 
the loads to be moved, it will be proper also to 
make known the passive resistance or friction of the 
movers which we have to employ ; for it is only the 
surplus of their power over and above what is 
necessary to propel themselves, that these movers 
can apply to the drawing of burdens. 

While a locomotive engine is performing the 
traction of a train, it evidently requires: — 1st, a 
certain force to make the train advance, or to over- 
come the resistance of all the loaded carriages ; and 
2dly, another force to propel itself by overcoming 
its own friction. It is this second force, that which 
causes the engine to move, which represents the 



FRICTION OF UNLOADED ENGINES. 201 

friction of the engine ; whereas the first is the resist- 
ance of the load^ and the union of the two efforts 
constitutes the total force applied by the mover. 

The friction of a locomotive engine is then the 
force it expends to maintain itself in motion on the 
rails. But that force must clearly vary according 
to the weight or resistance of the load which the 
engine draws. In effect, the greater that weight, 
the greater also will be the pressure it causes on the 
axes of rotation, and on the divers moving parts of 
the apparatus ; and as the friction is always in pro- 
portion to the pressure, it follows that the friction 
which takes place at these points, must augment with 
the load. Hence the friction of the engine, which 
is nothing more than the force resulting from the 
union of these different frictions, must equally 
increase with the load. 

Thus, we shall first establish a difference between 
the friction of an engine unloaded^ and that of the 
same engine loaded. 

On the other hand, the force requisite to set in 
motion an unloaded engine may itself be decomposed 
into two portions arising from two distinct causes : 
Ist, that which is necessary to overcome the friction 
of all the parts of the apparatus itself, and which 
would be observed if the engine were supported on 
its axles and did not propel its own weight along the 
rails ; and 2dly, that which is necessary to execute 
the progressive motion, that is, to overcome the 



202 CHAPTER VIII. 

particular friction caused on the axles and wheels 
by the weight of the engine, as in other carriages. 

Finally, then, we will consider the fiiction of a 
locomotive engine, under any circumstances what- 
ever, as composed of the three following resistances : 

1st. The resistance due to the friction of its 
mechanical organs. 

2d. The resistance arising from the weight of the 
engine, considered as a carriage. 

3d. The additional friction, caused in the engine, 
by the load it draws. 

If we knew these three elements of the total 
resistance separately, it is plain that we could, 
under all circumstances, conclude from them the 
friction of a locomotive engine whose construction, 
weight and load, were known. These must then be 
the present object of our inquiry. 

To attain our end, we shall first seek to determine 
the friction of unloaded engines, which is the sum 
of the two first of the resistances mentioned above ; 
and deducting from this the resistance of the engine 
considered as a carriage, which may easily be done, 
since in this respect the engines may be assimilated 
to waggons, we shall obtain the friction of the me- 
chanical organs of the engine. Thence we shall 
pass to the second part of our inquiry, which will 
consist in determining the additional friction of the 
engines, according to the load they draw. 



FRICTION OF UNLOADED ENGINES. 203 



Sect. II. Of the different modes of determining the 

friction of unloaded engines. 

The force necessary to move an unloaded loco- 
motive engine may differ according to two different 
circumstances : 

1st. The steam remaining shut in the boiler, and 
having no access to the mechanism nor exerting 
any pressure on it, so that the progression of the 
engine be produced by an external agent. 

2nd. The steam being the agent which produces 
the motion. 

The difference between these two cases cannot 
be very great ; for in both circumstances the load 
of the engine remains the same, being no other 
than its own weight. Besides, whatever be the 
means that make it move, it goes forward; thus 
at each turn of the wheel there is a complete 
revolution, and therefore a complete friction, of 
all the mechanism. The steam, in order to move 
the engine, would have applied a certain force. 
That force would have produced pressure, and con- 
sequently proportional friction, on all the points 
compressed. Now, the moment we make the 
engine advance, we apply a force equal to that 
which the steam would have applied. Thus we 
produce on all the joints the same pressure, and 
consequently the same friction, as the force of the 
steam would have produced. Of all these joints 



\ 



204 CHAPTER VIII. 

or moving parts, it is only those, therefore, whereon 
the steam acts in a direct and particular manner, 
which are not equaUy compressed in both cases. 
These parts being strongly pressed one against the 
other when the steam is admitted into the cyUnders, 
cease to experience that pressure, and in conse- 
quence have indisputably less friction, when the 
steam takes no part in creating the motion. But 
the parts on which the steam exerts a direct pres- 
sure are merely the two slides. 

The surface of the slide, on which the pressure of 
the steam acts, is generally 7^ inches by 6, or 45 
square inches; which makes 90 square inches for 
the two slides. When we suppose the engine 
moving alone, and without drawing any train after 
it, we cannot suppose that the effective pressure 
of the steam in the boiler need be more than 
10 lbs. per square inch. We shall see by experi- 
ment that it may be no more than 4 or 5 lbs. The 
pressure made by the steam on the slides is then, 
at most, 900 lbs. Taking the friction of iron 
against iron, poUshed and lubricated with oil, at 
^Q of the pressure, it would be a friction of 90 fbs. 
But it is well known that a force appUed at one 
point of an engine, when transmitted to another 
point of the same engine, changes its intensity in 
the inverse ratio of the velocity of the points con- 
sidered. The slide moves but 3 inches at each 
stroke of the piston, or ^ foot at each turn of the 
wheel, that is to sav, it traverses but ^ a foot, while 



FRICTION OF UNLOADED ENGINES. 205 

the engine, having a wheel of 5 feet in diameter, 
advances 15*71 feet. The friction of the slide, 
therefore, considered as opposing the motion of 
the engine, creates at most a definitive resistance 

of ^^t 2^ — , ^ 1, 1 or about 3 fts. Whence it is 
2 X 1571 

seen that in practice the friction determined, either 
in the first case, or in the second, may be con- 
sidered as the true friction of the engine when it 
draws no load. 



Sect. III. Fricton of the engines determined by the 
smallest pressure of steam necessary to keep them 
in motion. 

The reflections developed above, and tending to 
prove that the force necessary to move an engine is 
sensibly the same, whether the power of the steam 
itself be employed to set it in motion, or any 
external agent be used, gave us three means of at- 
taining the knowledge of the friction of the engines 
when drawing no load. The first consisted in seek- 
ing what was the least pressure of steam requisite 
for a locomotive to maintain itself in motion on the 
rails, when it had no more than its own friction to 
overcome ; the second was the use of the dynamo- 
meter ; and the third was the method of the angle 
of friction, already employed with respect to wag- 
gons. All three were tried successively. 



20(5 CHAPTER VIII. 

The principle on which the first of these methods 
is founded is this : if the steam, exerting a known 
effective pressure per square inch, or per unit of 
surface of the piston, be found sufficient to keep 
the engine in motion, at a velocity however small, 
but yet at a uniform velocity, it follows that the 
effort then developed is just sufficient to hold the 
friction of the engine in equilibrio ; for if it were 
greater, the velocity would increase, and were it 
less, the velocity would diminish. In this case, 
then, in order to obtain the measure of the friction, 
it suffices to calculate the effort applied by the 
engine, which is easy, since the area of the two 
pistons is known, as well as the pressure exerted 
by the steam per square inch of their surface. 

It must only be observed, according to the prin- 
ciple already mentioned, that the pressure exerted 
on one part of an engine, on being tmnsmitted to 
another part of the same engine, reduces itself in 
the inverse proportion of the velocity of the points 
of application. In the case before us, the velocity 
of the engine is to that of the piston, as the circum- 
ference of the wheel is to twice the stroke, since the 
piston makes two strokes while the wheel performs 
one turn. A force applied on the piston produces 
then, for the progression of the engine, only a force 
reduced in the inverse proportion of these velocities, 
that is to say, as twice the stroke is to the circum- 
ference of the wheel. 



FRICTION OF UNLOADED ENGINES. 207 

Let d be the diameter of the piston, ^ird^ will be 
the area of one of the two pistons ; P-^p being the 
effective pressure of the steam per unit of surface, 

will be the effective pressure on both pistons. If, 
moreover, / express the length of the stroke of the 
piston, and D the diameter of the wheel, the effec- 
tive force of translation resulting for the engine, in 
virtue of this pressure, will be then 

^ird^ (P -i>) X ^ or £' , 

which, from what has been said, will give the 
measure of the friction of the engine. 

It must be noted, that the pressure of the steam 
in the cylinder is here taken as equal to that which 
exists in the boiler. The reason of it is that, in 
the experiments which we shall have to make by 
that mode, the motion of the engines being always 
extremely slow and the regulator entirely open, the 
two pressures will have time to settle in equilibrio, 
and therefore will be equal to each other. 

To ascertain the smallest pressure capable of 
moving the engine, it was necessary to take that 
engine at a time when it was producing steam at 
a very low degree of elasticity. The evening, after 
the work was done, and the fire thrown out of the 
fire-box, when the water in the boiler was beginning 
to lose its heat, and the steam arising from it was 



208 CHAPTER VIII. 

gradually losing its force, was the moment favour- 
able for trying the smallest pressure at which the 
engines could move along the rails. The spring- 
balance, which closed the safety-valve, showed the 
pressure of the steam in the boiler, by loosening 
the spring till it was precisely in equilibrio with 
that pressure; and to make the observation more 
sure, the engine was immediately brought to the 
stationary syphon-manometer, and that instrument 
gave the true pressure per square inch in the boiler 
at the moment of the experiment. In this manner 
were made the following experiments, of which we 
shaU only give the first in detaU. 

On the 5th July, 1834, the engine Atlas, cylin- 
der 12 inches, stroke of the piston 16 inches, weight 
11*40 tons, wheels 5 feet, 4 wheels coupled, was 
submitted to the experiment separate from its 
tender. 

The spring of the balance being loosened more 
and more, to show the pressure of the steam in the 
boiler, as it gradually lowered, the following trials 
were made. 

At 2 lbs. of pressure marked on the balance, the 
engine moved forwards and backwards, passing from 
rest to motion, or surmounting, besides the friction, 
what is called the vis inertue of the mass of the en- 
gine ; that is to say, not only preserving an acquired 
velocity, but acquiring it ; which proves an excess 
in the moving power above the resistance. 

At Ifb. of pressure similarly marked, the engine 



\ 



FRICTION OF UNLOADED ENGINES. 209 

started, passing again from the state of rest to that 
of motion. 

The pressure still lowering a little, and the balance 
being at zero, the engine continued to move. At 
this moment it was brought under the manometer. 
The instrument marked 4 lbs. of effective pressure 
per square inch in the boiler, the valve then bearing 
merely the weight of the lever or something less, 
which was not discernible on the balance, as the 
lowest pressure it could indicate was that of the 
lever. 

The cyUnder being 12 inches in diameter, the 
area of the two pistons was 226 square inches. 
Thus a pressure of 4 tbs. per square inch produced 
on the piston a force of 226x4=904 lbs., that is 
to say, it could move a resistance of 904 lbs. at the 
velocity of the piston. But at the velocity of the 
engine, which is greater in the proportion of the 
circumference of the wheel to twice the stroke, or 

could overcome only a resistance of ^,g^^y' == 1 54 

tbs. 

Thus, as we have seen that the engine still moved 
at the moment when it was put under the mano- 
meter, though the pressure was then reduced to 
4fi>s., it is plain that the resistance of the engine 
did not exceed 1 54 lbs. 

This first experiment had been made with the 



J 



210 CHAPTER VIII. 

engine separate from its tender, with a view not to 
entangle one resistance with another; hut wishing 
to apply it to lighter engines with uncoupled wheels, 
an inconvenience occurred. The pressure necessary 
to move the engine alone without tender was sq low 
that the spring-balance could not indicate it, that 
pressure being less than the weight of the lever 
itself. Another inconvenience of this low pressure 
was, that it could not be obtained till the moment 
when the boiler produced no steam at all ; so that 
the pressure was then lowering so rapidly that the 
accuracy of the experiment could not be de- 
pended on. 

But as the resistance of the tender-carriage might 
easily be calculated from the experiments made on 
the friction of the carriages already inserted above, 
it was easy to take account of it. Thus the tender 
being left attached to the engine, the experiments 
offered the same degree of accuracy, with greater 
facility in observing the pressure of the steam. 
For this reason, in the following experiments the 
tender-carriage was no longer separated from the 
engine. 

These experiments were made in a manner entirely 
similar to the one we have just explained; save, 
that to deduce from them the firiction proper to the 
engine itself, we subtracted for the traction of the 
tender, first 6 fts. per ton, and again 1 lb. per ton 
for the additional friction which every ton of that 
load produced in the engine, according to what will 



FRICTION OF UNLOADED ENGINES. 211 

be seen in the second article of this chapter. We 
shall only, therefore, present in the following Table 
the elements and the results of these experiments. 
We have neglected the resistance due to the blast- 
pipe, on account of the slowness of the motion, and 
especially of the little vaporization which took place 
in the boiler. 






f 



212 



CHAPTER VIII. 












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FRICTION OF UNLOADED ENGINES. 213 

Sect. IV. Friction of the engines^ determined by the 

dynamometer. 

At the same time that the friction of the engines 
was determined in this manner, other essays were 
also made to obtain the valuation of that friction by 
means of the dynamometer. 

On the 22nd of July, the engine Vulcan, cyUnder 
11 inches, stroke 16 inches, wheels 5 feet, weight 
8*34 tons, one pair of wheels only worked by the 
piston, being ready to start for Manchester, its 
boiler full of water, and fire-box full of coke, was 
separated from its tender. A circular spring-balance 
was fixed to the engine, and a lever passed through 
the ring of the balance, for two men to draw the 
engine by means of the lever. 

The engine was first set in motion by five or six 
men. As soon as the first impulse was given, the 
two men at the -lever kept it in motion without 
difficulty at the velocity of between 2 and 3 miles 
per hour. The style of the balance oscillated 
considerably; it went generally from 130 fts. to 
170 lbs., giving a mean traction of 150Sbs. 

The balance was then taken off the front of the 
engine and fixed on the hinder part, then turned 
towards Liverpool, and the same experiment re- 
newed gave a mean traction of 140 fts. The style 
still oscillated, in general, some twenty pounds above 
and below that point. 

Mean of these two experiments 145 lbs. 



214 



CHAPTER VIII. 



The engine was ready to start, and had akeady 
taken a few runs on the rails to get up the fire and 
fill the boiler. Thus the greases which served to 
lubricate the rubbing parts were melted, and the 
oils quite liquid. But the experiments being made 
within the enclosure of the station, on a place of 
continual thoroughfare, where the rails are con- 
stantly covered with cinders and dirt, this circum- 
stance must have greatly augmented the resistance 
to the motion. 

We here subjoin the Table of three other ex- 
periments, made in a similar manner. 

Experiments on the friction of unloaded locomotive engines j 

by the dynamometer. 



Number 
of the 
experi- 
ment. 


Dmteoftbe 
experiment. 


Name of 
the engine. 


j 

Diune- - Stroke 
terofthe of the 
cylinder.' piiton. 


Diame- 
ter of the 
wheel. 


Weiffht 

of the 

engine. 


Friction 

of the 

engine. 








inches, inches. 


feet. 


tons. 


lbs. 


VI. 


July 22, 1834. 


Vulcan. 


11 


16 


5 


8-34 


145 


VIL 


July 23, 1834. 


Sun. 


11 


16 


5 


7-91 


115 


VIII. 


Do. 


FiBXFLT. 


11 


18 


5 


8-74 


127 


IX. 


Do. 


Fury. 


11 


16 


5 


8*20 


105 



Sect. V. Friction of the engines^ determined by the 

angle of friction. 

The results obtained by the dynamometer were 
not very far different from those obtained by the 
least pressure ; but as in all these experiments, the 



FRICTION OF UNLOADED ENGINES. 215 

style of the balance oscillated exceedingly, in con- 
sequence of the little inequalities of the way, or the 
jerks given by the men who drew the engine, it 
was very difficult to ascertain the mean traction. 
It was very desirable, therefore, to determine the 
friction of the engines by a different method, in 
which that cause of error should not exist. 

For this reason the engines were submitted to the 
same experiments that had served to determine the 
friction of the waggons. 

These experiments having been made and calcu- 
lated exactly like those on the waggons, we shall 
merely give their results in the following Table. 
Account was taken of the resistance of the air 
against the wheels, in the same manner as in the 
experiments on the friction of waggons. 



216 



CHAPTER VIII 



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FRICTION OF UNLOADED ENGINES. 217 

Sect. VI. Table of the results of the preceding ex- 
periments on the friction of unloaded engines. 

Finally, for the convenience of making researches, 
we unite the results of these different experiments 
in one Table. 



218 



CHAPTER VIII. 



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FRICTION OF UNLOADED ENGINES. 219 

In all these experiments we find that those made 
on the inclined plane give less friction than those 
made in the enclosure of the station, whether hy the 
dynamometer or hy the least pressure. This result 
has already been explained by the sand, cinders, or 
mud, which alwajrs cover the rails at the station ; 
but, on the other hand, in the experiments made on 
the inclined planes, if the regulator of the engine 
did not close the passage hermetically, a slight 
escape of steam may have taken place in the cy- 
linders, and in a certain degree favoured the motion 
of the engine. The results then of the two modes 
of experiment deviate contrary ways, and the dif- 
ference between them not being very considerable, 
we have reason to think that their mean gives the 
result required with an accuracy sufficient for 
practice. 

Examining these experiments, to deduce from 
them a general datum, and leaving out the engine 
Vesta, which was found to be in an exceptional 
case, we perceive that engines such as the Sun, 
Firefly, Vulcan, Fury, Leeds, and Jupiter, of 
an average weight of 8 tons, and with four wheels 
not coupled, have a mean friction of 104 lbs. 

That the engine Atlas, of the weight of 1 1 tons, 
having six wheels, four only of which are conical 
and with flanges, but coupled, has a friction of 
139 lbs. 

And finally, that the engine Star, of the weight 



220 CHAPTER VIII. 

of 1 1 tons, with six flanged wheels, has a friction of 
176 fts. 

We shall presently see that these differences de- 
pend in part on the weight of the engines. But it 
will readily be conceived that the friction being 
influenced by so many different circumstances, it is 
impossible to imagine that it can be identically the 
same, not merely in engines of a different con- 
struction, but even in engines perfectly similar to 
each other, and coming from the very same builders. 
The observed differences ought not then to surprise. 

Sect. VII . Of the friction of the mechanical organs 
of the engine^ and of its friction as a carriage. 

In the preceding paragraphs we have determined 
the friction of unloaded engines ; but we have 
already said that this friction is composed of two 
parts, viz., the resistance arising from the weight 
itself of the engine, considered as a heavy carriage 
to be drawn along the rails ; and that which results 
from the friction of the different parts of the me- 
chanism, and which would equally take place if the 
progressive motion did not exist. As the first of 
these two forces varies with the weight of the 
engine, and as the second, on the contrary, is 
nearly constant for engines of the same proportions, 
it will be proper now to estimate them severally in 
the total friction of the unloaded engine. 



FRICTION OF UNLOADED ENGINES. 221 

We have seen above that locomotives such as 
SuN^ Firefly, Vulcan, Fury, Leeds, and Ju- 
piter, have a mean friction of 104 lbs. In the 
state m which those engines were submitted to ex- 
periment, their load was their own weight. Now we 
know that a weight of 1 ton, carried on waggons 
with springs as we have described, opposes to the 
traction on a railway a resistance of 6fts., and we 
shall presently see that the effort of this traction 
creates, moreover, in the engine, an additional fric- 
tion of 162 X 6 lbs. = 97 ft. ; which makes in all 
7 fts. per ton. On the other hand, the engines, 
considered as carriages, are of a construction quite 
similar to that of the waggons. The wheels and 
axle-trees have not indeed the same dimensions in 
both cases. In the engines, the axle-bearings are 
somewhat thicker in proportion to the diameter of 
the wheels, which is disadvantageous as to the 
friction on the axle, but the difference is trifling; 
and again, the wheels of the engines being larger, 
offer somewhat less resistance as to the friction of 
rolling. Besides, they are greased, and kept with 
* more care. We may therefore, without any im- 
portant error, assimilate the engines to waggons 
with reference to their friction as carriages. Then 
it will be easy to deduce from the total friction of 
the engine the portion attributable to its weight, 
and the remainder will be the friction of the ma- 
chinery. The engines which have just occupied 
our attention, and whose friction is 104 fts., ai;e of 



i 



222 CHAPTER VIII. 

the average weight of 8 tons ; they create then, as 
carriages, a total resistance of 56 lbs., and conse- 
quently the friction of their mechanical organs 
amounts to 48fts. 

As to the Atlas engine, the passive resistance of 
which is 139 fts., the same calculation makes the 
friction of the mechanical organs amount to 59 fts. ; 
and there is room to think that the excess of this 
number above the preceding depends on the coupling 
of the wheels of the engine. 

With respect to the engine Star, we can draw no 
conclusion, for want of knowing precisely the fric- 
tion of a carriage borne on six flanged wheels, as 
that engine is. 

These calculations authorise us then to consider 
the resistance of the mechanical organs in engines 
of the kind described above, and when in good 
order, as being at a medium from 48 to 59fts. 

Consequently, to value in pounds the friction of 
an unloaded locomotive engine, the number 48, or 
the number 59, which, according as the engine has 
its wheels unconnected or coupled, represents the 
friction of its mechanical organs, must be added to 
its total friction as a carriage, which is no other 
than the product of its weight expressed in tons by 
the number 7. 

The same result will be attained approximatively 
by simply taking the friction of the engines at 1 5 lbs. 
per ton of their weight, that is, at twice and a half 
the friction of the waggons. 



ADDITIONAL FRICTION OF THE ENGINES. 223 

This manner of estimating the (riction of the 
engines is useful whenever it is wished to calculate 
the effect that may be expected finom them, without 
having recourse to an immediate experiment. But 
it is espedaUy necessary, when, before constructing 
a locomotive, it is required to determine the pro- 
portions it ought to have in order to produce desired 
effects. In this case, indeed, the calculation cannot 
be performed without emplo3ring in it the presumed 
friction of the engine, and as the weight intended 
for the engine is always decided previously, it will 
be easy to derive the friction it will have, if it be 
properly constructed. 



ARTICLE II. 

OF THE ADDITIONAL FRICTION OF LOADED LOCO- 
MOTIVE ENGINES. 

Sect. I. Of the mode of determination. 

We have just determined the friction of loco- 
motive engines when they draw no load but their 
own weight. But those engines are never employed 
in that way, and we have shown that the friction of 
the same engine must become greater as it draws a 
greater weight ; because the augmentation of weight 
increases the pressure exerted on the different 
moving parts of the apparatus, and with the pres- 
sure increases necessarily also the corresponding 
friction. We shall now, therefore, endeavour to 



224 CHAPTER VIII. 

determine the precise value of this surplus of re- 
sLstance produced in the engine by virtue of the 
load which it draws. 

When an engine performs the traction of a train, 
the pressure of the steam in the boiler is known 
finom inspection of the manometer or of the balance 
of the safety-valve. But the pressure of that steam 
in the cylinder is not known, because in passing 
from the boiler to the cylinder it alters its elastic 
force, as will be seen further on. If the pressure in 
the cylinder could be known a priori, — ^if, for in- 
stance, it were possible to apply a manometer to 
the cylinder, then would immediately be deduced 
what is the friction of the engine corresponding to 
that load. 

In effect, since by h3rpothesis the pressure in the 
cylinder or on the piston would be known, calcu- 
lating the total effect of that pressure on the area of 
the piston, we should have the exact valuation of 
the power applied by the engine. Now, from other 
sources is known also the resistance opposed to 
the motion, for it consists of the gravity, the fric- 
tion of the train, the resistance of the air, the 
resistance caused by the blast-pipe, and the friction 
of the engine. 

Besides, if the engine, in drawing this load, were 
constantly to increase its velocity, there would 
plainly be excess of the power over the resistance ; 
if, on the contrary, the velocity were gradually to 
lessen, the power would be inferior to the resist- 



ADDITIONAL FRICTION OF THB ENGINES. 225 

ance ; but if the engine be observed at a moment 
when it has acquired a certain uniform velocity, and 
that velocity be maintained without alteration, the 
effort then applied by the engine must necessarily 
be precisely equal to the resistance which is op- 
posed to it; for, were it not so, there would be 
acceleration or retardation of motion. 

Thus, the effort appUed by the engine and the 
resistance opposed to the motion would be known, 
and by making these two quantities equal to each 
other, we should thence deduce the friction proper 
to the engine. 

This mode then would give immediately the fric- 
tion of the engine, if the pressure in the cylinders 
were known. 

But there are cases wherein the pressure in the 
cylinder is in effect known ct priori, and is no other 
than the pressure in the boiler itself. These cases 
are those wherein the engine attains the limit of its 
power with the pressure at which it works, that is 
to say, when it draws the greatest load it can draw 
with that pressure. 

In effect, since by hypothesis the engine has 
attained the limit of its power, the pressure in the 
cylinder cannot be less than in the boiler ; for if it 
were, by diminishing the velocity, which is the only 
obstacle to the equiUbrium of pressure being esta- 
blished between the two vessels, we might give the 
steam time to rise in the cyUnder to a pressure equal 
to that of the boiler, and then the effect would be 

Q 



226 CHAPTER VIII. 

augmented. That is to say, the engme would draw 
a greater load, which is against the hypothesis. On 
the contrary, as soon as the pressiire in the cylinder 
is hecome equal to that of the boiler, no subsequent 
diminution of velocity will admit of increasing the 
load ; for that increase of load requires an increase 
of intensity in the motive force, that is, in the 
pressure of the steam on the piston, which is no 
longer possible. 

Thus, in the case wherein the maxunum load of 
the engine is attained, we know it priori the effort 
applied, and can, as has been explained above, 
deduce from thence the corresponding friction of 
the engine. 

Suppose then, in an experiment, this limit of the 
power of the engine to be attained. Let d be the 
diameter of the piston, and w the ratio of the cir- 
cumference to the diameter, lird^ will be the area 
of one piston, and j^ird^ the area of the two pistons 
together. Again, let (P— |>) be the effective pressure 
of the steam, per unit of surface, during the experi- 
ment ; it is clear, from what has been said above, 
that ^ird^ (P— i^) will be the force which was then 
applied on the piston. 

Calling D the diameter of the wheel, and I the 
length of the stroke, that force applied on the 
piston was, on transmitting itself to the engine, 
reduced in the inverse ratio of the respective veloci- 
ties, or in the ratio — =r. Thus, after transmission 

ttD 

to the engine, it had for its expression : 



ADDITIONAL FRICTION OF THE ENGINES. 227 

This is then the expression of the force of traction 
appUed to the progression of the engine. 

Again, expressing by p'v the effective pressure 
produced on the opposite face of the piston by the 
action of the blast-pipe, the resistance thence re- 
sulting against the progression of the engine was 

, dH 

Similarly, M being the weight of the load, and m 
that of the engine, both expressed in tons, g the 
gravity, in pounds, of a ton placed on the incUned 
plane of the experiment, and, in fine, k expressing 
the friction of the carriages per ton, 

{k + g)M + gm 

was the resistance opposed by the friction and the 
gravity, in ascending the inclined plane. Finally, if 
uv^ represent the resistance of the air, at the velo- 
city of the motion, and X the unknown friction of 
the loaded engine, we see that 

{k + g)M + gm + uv^ +P^^ + X 

was the total resistance opposed to the motion of the 
engine. 

As we have seen that, by reason of the uniformity 
of the motion, the power was equal to the resistance, 
it follows that we had 



228 CHAPTER VIII. 

(P-p) ^= (k + g)M + gm + uv^ + p'v^+X, 

and consequently, in fine, 

X = (P^p^p'v)^^{k + g) M-gm^uv'. 

This equation therefore gives the friction of the 
loaded engine. 

To apply this expression to the numerical deter- 
mination of the friction, attention must be paid to 
the manner of expressing the different quantities 
contained in it. P represents the total pressure of 
the steam in the boiler, p the atmospheric pressure, 
and p'v the effective pressure owing to the blast- 
pipe ; and these forces act against the surface of the 
piston. Thus, according as they are expressed in 
pounds per square inch, or in pounds per square 
foot, the diameter d of the piston must be measured 
in inches of in feet. The length I of the stroke, and 
the diameter D of the wheel, must be expressed 
either both in feet or both in inches, which is 
indifferent, since the equation contains only their 
ratio. The quantities fc, g and uv^ must, as we have 
said, be expressed in pounds, and in fine the defini- 
tive value of X will equally be expressed in pounds. 

Sect. II. Experiments on the additional friction of 

locomotive engines. 

The formula which we have just obtained is very 
simple, and gives easily the friction of the engine 
in all cases when it has attained the limit of its 



ADDITIONAL FRICTION OF THE ENGINES. 229 

power. All that remains to do, then, is to attain 
that point. In consequence, we undertook a series of 
experiments, sometimes taking the loads as great as 
the engine could draw, at other times limiting our- 
selves to a moderate load, but lowering the pressure 
in the boiler by means of the safety-valve, as much 
as possible without stopping the train. 

The experiments in question were made on three 
inclined planes of the Liverpool and Manchester 
Railway, viz.: on the inclined plane of Sutton, 
inclined ^, on that of Whistoriy inclined ^^ and 
on the acclivity of ChatmosSy rising f^^o- ^ ^ti- 
mating the resistance on these planes, we took 
account of the gravity, as has been indicated in 
Chapter VI. As to the resistance of the air and 
that df the blast-pipe, we used the practical Tables 
which we have given on the subject. For that 
purpose, we note, in each experiment, the elements 
proper for the use of the Tables, viz.: the velocity of 
the engine, the mean vaporization of the boiler, the 
area of the blast-pipe, and the nature of the train in 
motion. With these data, there is no difficulty in 
finding, without calculation, the quantities which 
we have expressed above by uv'^ and pv ; and sub- 
stituting them, with the dimensions of the engine 
and the other data of the problem, in the formula 
developed above, we thence conclude the additional 
friction of the engine. 

The results thus obtained in the different experi- 
ments now before us, are collected in a Table which 



230 CHAPTER VIII. 

we shall presently offer : to show however the pro- 
ceeding which we have followed, and to make the 
nature of it better understood, we will here detail 
the calculation of the first of those experiments. 

On the 22d July, 1834, the engine Vulcan, 
cylinder 11 inches, stroke of the piston 16 inches, 
wheel 5 feet, weight 8*34 tons, effective pressure in 
the boiler then 57*5 lbs. per square inch, ascended 
the inclined plane of Sutton with a train of 6 first- 
class coaches, the mail, and two empty trucks; 
weight of the train, tender included, 39*07 tons. 
The velocity of 26*6 miles per hour^ before reaching 
the foot of the inclined plane, sunk to 7*5 miles per 
hour at the top of the plane. 

With these data, we have to calculate succes- 
sively the effort appUed by the engine, and the 
resistance which was opposed to it. Now, the 
effective pressure observed in the boiler, was 57*5 
fts. per square inch. Moreover, in this engine the 
diameter of the blast-pipe was 2*25 inches, and the 
mean vaporization 60 cubic feet of water per hour. 
Consequently, from the Table given above, the re- 
sistance against the piston, caused by the blast-pipe, 
at the velocity of 7' 5 miles per hour, was 1*3 ft. 
per square inch. The real disposable force of the 
engine then was 57*5 — 1*3= 56*2 fts. This is 
the quantity which we have represented above by 
(P—p—pv), 

This premised, the effort exerted by the engine 
might be calculated thus : 



ADDITIONAL FRICTION OF THE ENGINES. 231 

1 90 . . . Area of the two pistons, in 
square inches^multiplied by 
56'2fts. Real effective pressure of 
the steam per square inch 
on the piston, gives 
10678 lbs. Force appUed on the pis- 
ton; which, transmitted as 
force of traction to the en- 
gine, whose velocity is 59 
times as great, gives 

= 1810 lbs. Definitive effort applied by 

the engine. 

On the other hand, the resistance was : 

3907x6=234 lbs. Resistance owing to the 

friction of the carriages. 

^Q =1193 lbs. Resistance caused by the 

gravity of the total mass, 
train and engine, on the 
plane inclined ig ; 
25fts. Resistance of the air against 
an effective surface of 1 70 
square feet, at the velocity 
of 7*5 miles per hour. 

1452 lbs. Total resistanceof the train. 

Consequently, subtracting first the resistance of 
the train from the effort exerted by the engine, we 
have 



232 CHAPTER VIII. 

1810 
-1452 

358 lbs., 

which is the total friction of the engine, corre- 
sponding to the above load. Moreover, if we again 
subtract 125 lbs. for the friction of the unloaded 
engine, there remains 

358 
-125 

233 lbs.; 

and this number consequently indicates the addi- 
tional friction created in the engine by the resistance 
of 1452 lbs. Finally, then, the additional friction 
created by each pound of resistance or of traction 
imposed on the engine, is 

233 



1452 



= 161 ft. 



The other calculations are performed in a manner 
entirely similar. For this reason we content our- 
selves with presenting the data and the results of 
them in the following Table. 

We have made a distinction between the engines 
with uncoupled wheels, and those with coupled 
wheels, because it is evident that in the latter, 
whose wheels are held together by connecting rods, 
the motion is communicated by a greater number of 
joints, and consequently all that tends to produce 
an additional friction must produce a more con- 
siderable one in them than in the engines with 
unconnected wheels. 



ADDITIONAL FRICTION OF THE ENGINES. 233 







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234 CHAPTER VIII. 

From these experiments, we perceive that in 
engines with uncoupled wheels, the additional 
friction created per ft. of traction is '137ft., that 
is to say, the friction is about j- of the resistance 
imposed on the engine; and that in engines with 
coupled wheels it amounts to '215ft., or may be 
taken at half as much more than the precedmg. 
It will readily be conceived, however, that it must 
vary with the construction and state of every en- 
gine. This is observable particularly in the engine 
Vesta, which, at the moment of the experiments, 
was not in a state of repair altogether satisfactory. 

With reference to the manner in which the addi- 
tional friction of engines ought to be calculated, we 
have to recall to mind that it is to be reckoned on 
every pound of the total resistance exerted against 
the motion ; that is to say, the resistance caused by 
the friction of the waggons, that of gravity, and that 
of the atmospheric air, must first be calculated, and 
on the sum of these the additional friction of the 
engine is to be taken at the rate already indicated. 
It was in fact only by first introducing these dif- 
ferent resistances into the account, that we have 
attained the above result; and consequently there 
can be no misunderstanding as to the manner in 
which the calculation should be done. 

With respect to the resistance created directly on 
the piston, either by the atmospheric pressure or by 
the pressure arising from the blast-pipe, as these 
forces are destroyed by the opposed pressure of the 



ADDITIONAL FRICTION OF THE BNGINES. 235 

steam immediately, without the interposition of any 
action on the part of the mechanical organs of the 
engine, it is evident that they can create no addi- 
tional friction in the engine. They ought not there- 
fore to enter into this account. 



Sect. III. New developements on the mode of deter- 
mination employed. 

An increase of friction in proportion to the load 
is foimded on principle, as we have proved, and the 
mode of calculation which we have used will give 
exactly the measure of it, provided the engine be 
really arrived at the limit of its power with a given 
pressure, that is to say, at the m,aximum load that it 
can draw at that pressure. For the cases in which 
the engine slackened its velocity to the rate of 2 or 
3 miles per hour, that point was evidently attained, 
since the engine was literally on the point of stop- 
ping. But moreover, it will presently be seen that 
for all cases in which the uniform velocity did not 
exceed 10 or 12 miles per hour, we were equally 
justified in taking the pressure on the piston as 
equal to that in the boiler. 

In effect, the steam being at a certain degree of 
pressure in the boiler, passes into the steam-pipe, 
and from thence into the cylinder, where it at first 
expands, and would promptly rise to the same de- 
gree of pressure as in the boiler, if the piston were 
immoveable. This piston, however, offering on the 



236 CHAPTER VIII. 

contrary but a certain resistance determined by the 
load which the engine draws, 40fts. per square 
inch for instance, will recede as soon as the elastic 
force of the steam in the cylinder shall have at- 
tained that point. A piston which withstands a 
resistance of but 40 lbs. per square inch, is nothing 
more than a valve loaded with 40 lbs. per square 
inch. If the communication between the boiler and 
the cylinder were completely open and without tube 
or contraction, the piston would become in reality a 
valve to the boiler ; and that valve yielding before 
the safety-valve which is loaded, for instance, with 
50fts. per square inch, the steam in the boiler 
could not rise above 40 lbs. As, however, the 
passage is contracted, the piston is not a valve 
to the boiler; but it still remains one for the 
cylinder. 

From these three points it results : 1st, that the 
pressure in the cylinder is strictly equal to the re- 
sistance on the piston ; 2ndly, that it is because the 
piston gives way and recedes before the steam, that 
the latter qannot augment its pressure beyond that 
point, and rise to the pressure of the boiler ; but if 
by any means whatever the piston were rendered 
immoveable, or only that it did not give way faster 
than the steam is generated at the pressure of the 
boiler, an equilibrium of pressure would at once be 
established between the cylinder and the boiler ; and 
3rdly, that if there be in the steam-pipe a velocity 
greater than that which corresponds to the velocity 



ADDITIONAL FRICTION OF THB ENGINES. 237 

of generation of steam in the boiler, it is because the 
pressure is less in the cylinder than in the boiler, and 
that the fluid consequently seeks to settle in equili- 
brio in the two vessels. These observations show that 
the eflfective pressure on the piston may be calcu- 
lated by that which exists m the boiler, as soon as 
the velocity of the piston is reduced to that of the 
generation of the steam. As we shall soon know by 
experiment, what is the total mass of steam, at the 
pressure of the boiler, produced by the engine in a 
given time, it will be easy to calculate how many 
cylinders full of steam, at that same pressure, the 
engine can supply in a minute, and thus what is 
the velocity which corresponds to what we call fall 
pressure in the cylinder. We shall then see that for 
the engines under consideration, it is from 10 to 12 
miles per hour, or thereabout. We may then con- 
sider that, in all the cases of uniform motion, 
wherein the velocity did not exceed that rate, the 
pressure in the cylinder was the same as that in the 
boiler; and therefore, in so calculating it, we had 
the exact measure of the power then applied by the 
engine. 



CHAPTER IX. 

OF THE TOTAL RESISTANCE ON THE PISTON. RE- 
SULTING FROM THE DIVERS PARTIAL RESIST- 
ANCES PRECEDENTLY MEASURED. 

Wb have just estimated successively, in the pre- 
ceding chapters, the divers resistances which oppose 
the motion of the engine. It is necessary now to 
seek the definitive resistance which results from 
them united, per square inch or per unit of surface 
of the area of the piston. 

The resistances which we have hitherto con- 
sidered are : the resistance of the air, the friction 
of the waggons, the gravity, the friction of the 
engines, and the resistance arising from the hlast- 
pipe. But we must here add, besides, the atmo- 
spheric pressure ; for the engines under consideration 
being high-pressure engines, it follows that the op- 
posite face of the piston necessarily supports, like 
every other body in conununication with the atmo- 
sphere, a certain pressure due to the elasticity of 
the atmospheric air. 

In the calculations which we have hitherto made, 
we were enabled to suppress that force in the re- 
sistance, because at the same time we equally sup- 



OF THE TOTAL RESISTANCE ON THE PISTON. 239 

pressed it in the power, by calculating the latter 
only according to the effective pressure of the steam, 
that is to say, according to its siurplus over the 
atmospheric pressure. This mode of proceeding 
was correct then, because, having to consider the 
power and the resistance only in the case of equality 
or equilibrium, and unmixed with any other con- 
sideration, we could without error retrench on both 
sides the same quantity. But as, in other questions 
which are about to present themselves, we shall 
want to consider the steam with reference to its 
volume, and as that volume depends on the total 
pressure at which the steam is generated, we must 
retain that total pressure, to express the elastic 
force of the steam ; and consequently, must also let 
the atmospheric pressure remain in the resistance 
opposed to the motion of the piston. 

Thus, the definitive resistance exerted against the 
piston consists of six resistances, which are : the 
friction of the waggons, the resistance of the air, 
the gravity of the train, the friction of the engine^ 
the atmospheric pressure, and the pressure caused 
by the blast-pipe. Of these six resistances, the last 
two act immediately and directly on the piston. 
They must therefore be moved at the velocity of 
the piston itself; but it is not so with the other 
four. It has already been said that in an engine, 
the pressures exerted on different points by the 
same force, are in the inverse ratio of the velocities 
of those points. Here the engine and its train must 



240 CHAPTER IX. 

be moved at a velocity greater than that of the 
piston, in the proportion of the circumference of 
the wheel, to twice the length of the stroke. The 
intensity of the pressure exerted by the resistance 
of the load, the air, the engine, and the gravity, is 
then increased by its transmission to the piston, in 
the above ratio of the velocity of the wheel to that 
of the piston. 

Consequently, if M express the number of tons 
gross which compose the total load, that is to say, 
including the weight of the tender-carriage of the 
engine, and k the number of pounds requisite to 
draw one ton on a railway, 

kU 

will be the resistance, in pounds, resulting from the 
friction of the waggons which carry the load. If at 
the same time we call g the gravity of 1 ton on the 
inclined plane to be traversed by the engine, and if 
m represent the weight of the engine, in tons, 

g {M + m) 

will be the resistance, in pounds, produced by the 
gravity of the total mass, train and engine ; so that, 
according as the motion takes place in ascending or 
in descending, the definitive resistance arising from 
friction and gravity will be 

kM±g (ML + m) = {k±g)M± gm. 

Similarly, if we express by uv^ the resistance, in 
pounds, exerted by the air against the train, at 
the velocity v of the engine. 



OF THE TOTAL RESISTANCE ON THE PISTON. 241 

{k ± g) M ± gm-^- uv^ 

will be the resistance opposed to the motion of the 
.engine by the friction, the gravity, and the shock of 
the air. 

If, again, F represent the friction of the unloaded 
engine, expressed also in pounds, and S its additional 
friction, measured as a fraction of the resistance, as 
has been indicated in Chap. VIII., we see that 

F + S[(k±g)M±gm + uv^] 

will be the total friction of the engine at the moment 
when it draws the resistance 

(fc ± jr) M ± jfm + wv^« 
Consequently 

(1 + S) [(ft ±g)M±gm + uv^] + F 

will be the total resistance opposed to the progres- 
sion, along the rails, by the engine and its train. 

As this force produces on the piston a resistance 
augmented in the ratio of the circumference of the 
wheel to twice the stroke of the piston, if D express 
the diameter of the wheel, I the length of the stroke, 
and w the ratio of the circumference to the diameter, 

vD ttDF 

(1 +8) [(fcljr) M ±srm + Mt;T -2|- + -gT 

will be the resistance on the piston, caused by that 
force, that is to say, caused by the resistance of the 
waggons, the gravity, the air, and the friction of the 
engine. 

R 



242 CHAPTER IX. 

This resistance is that which is exerted on the 
totality of the area of the pistons. But representing 
by d the diameter of the cylinders, ^ird^ will be the 
area of the two pistons. Whence 

ttD . •jtDF 

(1 + S) [(& ±g)M±gm + uv^] -^ + -^ 

or, simplifying, 

D . DF 

(1 + S) [(fc ±g)M±gm + wt;^ ^ + -^j> 

will be the same force, divided according to the unit 
of surface of the piston. 

Adding to this the atmospheric pressure ji, and 
the pressure caused by the blast-pipe j> v, which are 
already measured per unit of surface, we shall have 
in fine, for the total resistance R exerted on the 
piston, 

D DF 

R=(l+S)[(fc±(/)M±(7m+iit;^] -^^i+^+P+pv. 

In this expression, the quantity g represents the 
gravity on the plane to be traversed by the train ; if 
the plane be horizontal instead of inclined, we shall 
have 5^=0. The weights M and m of the train and 
the engine are expressed in tons gross ; the quantity 
k^ which is the friction of the waggons per ton, is 
equal to 6ibs. ; the value of S is '137 or -f* for 
engines with uncoupled wheels; the velocity t; of 
the engine is expressed in miles per hour ; in fine, 
according as the dimensions D, / and d are expressed 



OF THE TOTAL RESISTANCE ON THE PISTON. 243 

in inches or in feet, and the forces w, p and p\ in 
pounds per square inch, or in pounds per square 
foot, the value R which will result from the calcu- 
lation will be the resisting pressure on the piston, 
expressed likewise in pounds per square inch, or in 
pounds per square foot. 

Applying this calculation to a train of 9 waggons 
and a tender, weighing 50 tons gross, and drawn at 
the velocity of 20 miles per hour, up a plane in- 
clined 3^, by an engine with two cylinders of 1 1 
inches diameter, stroke of the piston 1 6 inches, pro- 
pelling wheels 5 feet, not coupled, weight 8 tons, 
friction 104 ibs., blast-pipe 2*25 inches in diameter; 
and referring, for the resistance of the air, to what 
has been said in Chapters IV. and VI., the proceed- 
ing will be as follows : 

50 X 6=300 fcs. Friction of the waggons, in 

pounds, or value of fcM. 

2240 

-Tjjw>X 58=260 ibs. Gravity of the total mass, 

train and engine, or value of 

g (M+m). 

194fts. Resistance of the air against 

an effective surface of 180 

square feet, at the velocity 

of 20 miles per hour, or 

value of let?*. 



754 fts. Resistance of the train, or 
(fc + S') M+jfm + Mi;^ 



244 CHAPTER IX. 

754Xl'137=857Ste. Resistance of the train, in- 
cluding the additional fric- 
tion which it produces in the 
engine, or 

+ 104 lbs. Friction of the unloaded en- 
gine, or F. 



961 fts. Total resistance to the pro- 
gressive motion of the en- 
gine, or value of the term 
(1+S) H]c+g)M+gm+uv'^+F. 

On the other hand, we have 

3- 1416 X 60 in.= 1885 Circumference of the wheel, 

expressed in inches, or wD. 
2xl6in.= 32 Double the stroke of the 

piston, expressed in inches, 
or 21. 



188-5 
32 



5*9 Ratio of the velocities of 
the wheel and the piston, 



or 



21 



Thus, 

961 X 5*9=5670 fts. Resistance produced on the 

piston, or value of the term 



OF THB TOTAL RBSISTANCB ON THE PISTON. 245 

Again, 

31416X11^ inn A 4- .1. f 

g = 190 Area of the two pistons, in 

square inches, or ^wd^. 

Consequently, we obtain in fine 

-ToQ =29'8fcs. Above-mentioned resistance, 

portioned per square inch 
of the surface of the piston. 

-f 3'5fi>s. Effective pressure per square 

inch, arising from the blast- 
pipe, or p'v. 

-{-14' 7 lbs. Atmospheric pressure per 

square inch, or p. 



48 '0 lbs. Definitive resistance, per 
square inch of the surface 
of the piston of an engine 
with two cylinders of 11 
inches in diameter, &c., 
when drawing a load of 50 
tons under the given cir- 
cumstances. 

Were it desired to know that resistance per square 
foot, it would suffice to multiply the last result by 
144, that is to say, the pressure required would be 
6912 S>s. per square foot, which number would have 
been obtained directly, if instead of expressing the 
area of the piston in square inches, and the partial 



246 CHAPTER IX. 

pressures ia pounds per square inch, these measures 
had been referred to the square foot as unit of 
surface. 

This example shows what is to be understood by 
the different quantities contained in the formula, 
and how each of them ought to be introduced into 
the calculation. 



CHAPTER X. 

OF THE VAPORIZATION OF LOCOMOTIVE ENGINES. 

Sect. I. Experiments on the vaporization of loco^ 

motive engines. 

So far our object has been to estimate the re- 
sistance offered to the motion of locomotives, ac- 
cording to the circumstances of their load and of 
their velocity. It will now be proper to value the 
power of which they can dispose to overcome that 
resistance ; and as we have already made known 
the means of measuring one of the elements of that 
power, viz., the elasticity or pressure of the steam 
in the boiler, it remains only to seek what quantity 
of that steam can be produced by the engine in 
different circumstances, and in a given time. 

For this purpose we undertook a series of expe- 
riments on the vaporization of locomotives, taking 
the engines successively either working without the 
aid of the blast-pipe, or with divers orifices of blast- 
pipe and different velocities, or, in fine, under 
different pressures in the boiler. We shall first 
give an account of these experiments, and then 
examine the influence of each of the circumstances 



248 CHAPTER X. 

just mentioned, on the vaporization produced by 
the engine. 

Among the experiments of which we are now 
going to present the results, the first three were 
made on engines at rest, and without the appli- 
cation of the blast-pipe, that is to say, without 
employing the waste steam in exciting the fire. 
The vaporization produced was therefore due simply 
to the natural draught of the chimney. In all the 
other experiments use was made of a blast-pipe, 
large or small, as will be seen indicated in the 
Table which we shall present further on. 

To know the quantity of water vaporized by the 
boiler, the proceeding was this. As all the tender- 
carriages of the Liverpool and Manchester Railway, 
on which the experiments were made, have exactly 
the same dimensions, it was ascertained first of all, 
by weighing one of them when empty and when 
full, that every inch of depth of the water in the 
tank corresponded exactly to a weight of 206'5fts., 
or 3*304 cubic feet of water. This established, the 
next thing done was to ascertain, by means of the 
glass-tube, the depth of the water in the boiler at the 
beginning of the experiment, and at the same time 
the exact depth was taken of the water contained 
in the tank ; afterwards, when the experiment was 
concluded, the boiler was first filled up to the height 
at which it was originally, and then the water re- 
maining in the tank was measured. The difierence 
between the two depths of water in the tank, gave 



OF THE VAPORIZATION OF THE ENGINES. 249 

the consumption that had been made of it during 
the time of the observation. 

As the experiments made with engines at rest, 
that is to say, without the application of the blast- 
pipe, show that in this state the engines are capable 
of effecting about ^ of their vaporization with the 
aid of the blast-pipe, use has been made of this 
datum to take account, in the different experiments, 
of the vaporization which had taken place during 
the stoppages of the engine, and during the descent 
of the inclined planes, on which the engines run of 
themselves, without making use of the steam. It is 
evident, in fact, that during this time, as well as 
during the delays which took place on the road, the 
fire was no longer excited by the action of the blast- 
pipe, and the vaporization was necessarily reduced 
in consequence. As the experiments took place on 
the Liverpool and Manchester Railway, which has, in 
each direction, a declivity of the kind we have just 
mentioned, and the descent of which, with the use 
of the brake, is performed in 5 minutes, we have, 
in all the cases, taken 5 minutes for the duration of 
the suspension of the action of the blast-pipe re- 
lative to that circumstance. Thus, for instance, in 
experiment VI., the engine Star stopped 15 minutes 
on the road. Besides this, the descent of the in- 
cUned plane occupied 5 minutes. Out of the total 
duration of the experiment, there were then 20 
minutes during which the action of the blast-pipe 
was suspended. As, during this time, the engine 



250 CHAPTER X. 

vaporized the same quantity of water that it would 
have done in 4 minutes, had it worked with the aid 
of the blast-pipe, it is plain that these 20 minutes 
of delay may be replaced by 4 minutes of forced 
vaporization. Thus the experiment is the same as 
if the 130*90 cubic feet of water consumed by the 
engine, had been vaporized in 1 hour 56 minutes of 
uninterrupted work; which gives 67*71 cubic feet 
for the vaporization effected per hour, during the 
appUcation of the draught of the blast-pipe. In 
this manner the numbers contained in the last 
column but one of the Table, were deduced from 
the observations. It is to be remarked, that the 
delays which took place during these experiments 
were caused by various essays made on the engines. 

To obtain the mean velocity of the motion, we 
divided the total distance performed, which was 
29*5 miles, by the total time of the experiment, 
minus the delajrs which took. place on the road; 
but in some experiments the engines ascended the 
inclined plane twice, which increased the total dis- 
tance performed to 32*5 miles instead of 29*5 ; and 
in those cases we have taken account of that cir- 
cumstance. 

In all the experiments we give the pressure m 
the boiler from direct observation. In experiments 
I. and II. the boiler was not placed on the engine, 
and was open to the air, that is to say, the steam- 
dome and the cover of the man-hole were taken 
off; so that the vaporization went on under the 



OF THE VAPORIZATION OF THE ENGINES. 251 

atmospheric presBure, or under an effective pressure 
null. 

' Before beginning any experiment^ we waited till 
the steam made the valves blow, which showed that 
the vaporization was in full activity; and in the 
experiments L and II., in which there was no valve, 
before beginning to note the quantity of water va- 
porized, we left the fire alight under the boiler for 
several hours, in order to be assured that the water 
effisctually boiled in all its parts ; and the non-ful- 
filment of .this condition made us reject several 
experiments. 

In fine, we give approximately the state of the 
temperature of the water in the tend^, at the mo- 
ment the engine started, because there must in- 
dubitably result firom it an increase in the definitive 
vaporization of the engine ; but as that temperature 
was not noted with sufficient accuracy, as it di- 
minishes, moreover, during the experiment, and 
lastly, as it may easily be compensated by a superior 
quality in the fud, or by more care on the part of 
the engine-man in stoking the fire, we are satisfied 
merely to point out its natural influence on the 
results, without seeking to take account of it with 
precision. 

In the following Table, which presents the results 
of these experiments, we group together those en- 
gines in which there is sensibly a like proportion 
between the heating surface of the fire-box and that 
of the tubes. The object of this distinction will be 



252 CHAPTER X. 

to seek, firstly, whether there results from it any 
difierence in the vaporizing power of the engines in 
a given time; and again, whether there results' 
therefirom any saving in the consumption of fuel in 
producing that vaporization. This second research 
will be the subject of the following chapter. 

It will be remarked that the Table contains two 
difierent engines of the name of Firefly. The 
reason is, as we have said elsewhere, that on re- 
constructing that engine, the dimensions of the 
boiler had been changed, and it wbs proper there- 
fore to distinguish the two engines by a different 
number. In like manner, the boiler under the 
name of Goliath II. was a new boiler, constructed 
to replace that which the engine had originally, and 
whose dimensions are given in the Table, page 37 
of this work. The new boiler, however, of the 
Goliath, instead of being placed on the engine for 
which it had been made, WBS used as a stationary 
boiler at the Edge-Hill station, on the Liverpool and 
Manchester Railway. It was there that we submitted 
it to experiment, with the aid of Mr. Edward 
Woods, now the Company's engineer, who is well 
known to evince as much skill as care in whatever 
researches he undertakes. 



OF THE VAPORIZATION OF THE ENGINES. 253 



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254 CHAPTER X. 

Sbct. II. Of the influence of the pressure in the 
boiler on the vaporization of the engine. 

In treating (Chapter II. of this work) of the laws 
which regulate the mechanical action of the steam, 
we have shown that the steam in contact with the 
liquid, under all degrees of tension, contains always 
the same total quantity of heat. Hence it follows, 
evidently, that to vaporize a given weight of water, 
under any pressure whatever, the same quantity of 
heat must always be communicated to it, that is to 
say, the same quantity of fiiel must be consumed in 
the same boiler ; and consequently too, a given 
consumption of fuel will always correspond to the 
vaporization of the same weight of water in the 
same boiler, whatever be the pressure under which 
that vaporization is effected. 

To comprehend clearly how it is that the steam 
can be generated at a higher or lower degree of 
pressure by the same application of heat, we must 
consider what passes in the boiler during the ebul- 
lition of the water. Suppose a boiler filled with 
water to a certain level, and containing, above that 
level up to the dome of the boiler, a vacant space of 
1728 cubic inches, capable of being filled with 
steam. Suppose, moreover, that the boiler be 
placed above a furnace filled with Ughted coal, 
emitting a certain quantity of heat per minute. As 
soon as the fire shall have transformed into steam 
1 cubic inch of the water contained in the boiler, 



OF THE VAPORIZATION OF THE ENGINES. 255 

the steam thus generated will fill the vacant space 
just mentioned; and since we have supposed the 
capacity of that space to be 1 728 cubic inches, that 
is to say, 1728 times the volume of the water va- 
porized, it follows that the steam which occupies that 
space will have a relative volume equal to 1728 
times the volume of the water. Now, recurring to 
the Table which we have given (Chapter II. of this 
work), and which is deduced irom experiment, it 
will be recognised that, when the relative volume of 
the steam is expressed by the number 1728, the 
total pressure of that steam is then about 15 lbs. 
per square inch, and its sensible temperature about 
212 degrees of Fahrenheit. Thus, at this moment, 
the steam contained in the boiler will be at the 
pressure of 15fbs. per square inch. Supposing 
then the safety-valve to be loaded only with the 
atmospheric pressure, which is also very nearly 
159>s. per square inch, we perceive that, if the 
safety-valve is large enough, the pressure in the 
boiler will never rise above that point, because the 
steam will escape by degrees as it is produced ; and 
consequently, whatever be the intensity of the fire, 
that is to say, in whatever quantity the steam be 
generated, it will still continue to be in the boiler at 
the pressure of 15fbs. per square inch, and at the 
corresponding temperature, or 212 degrees of Fah- 
renheit. 

But if we suppose the safety-valve of the boiler 
to be loaded with 50 9>s. per square inch, over and 



256 CHAFTBR X. 

above the atmospheric pressure, this is what will 
take place. At the moment when there is but one 
cubic inch of water vaporized, it will fill, as we have 
said, the vacant space in the boiler, and will be, as 
before, at the pressure of 15 lbs. per square inch, 
and at the sensible temperature of 212 d^;rees. 
But, as the fire continues its action, the steam 
being no longer able to escape by degrees as it is 
produced, on account of the resistance of the valve, 
the vaporized water will accumulate in the boiler, 
that is, in the same vacant space of which we have 
given the capacity. When, therefore, 2 cubic inches 
of water shall be vaporized, since these 2 cubic 
inches will still occupy a space of 1728 cubic 
inches, it is plain that the volume of the steam 
compared to that of the water which produced it, 
that is, the relative volume of the steam, will be 
expressed by the number 864. Hence, from the 
same Table above mentioned, the steam resulting 
fit>m the vaporization of these two cubic inches of 
water will be in the boiler at the total pressure of 
31 lbs. per square inch, and at the saasible tem- 
perature of 253 degrees, which corresponds to that 
pressure. As, however, the pressure of 31 lbs. will 
not suffice to raise the valve and admit of the steam 
escaping by degrees as it is generated, the steam 
produced by the action of the fire will continue to 
accumulate in the boiler. When 3 cubic indies of 
water shall have been vaporized, the pressure in the 
boiler will be 48 Jb&. per square inch, and the t^n- 



OF THE VAPORIZATION OF THE ENGINES. 257 

perature 280 degrees ; and, in fine, when there 
shall be 4 cubic inches of water transformed into 
steam, the pressure will have risen to 65 lbs. per 
square inch, and the temperature to 299 degrees of 
Fahrenheit. But at this moment the pressure of 
the steam will have become equal to the weight of 
the valve, and, in consequence, the latter will be 
raised. Whence, reckoning from this moment, and 
provided the safety-valve be large enough, the pres- 
sure and the temperature of the steam will continue 
to maintain themselves at the same degree, what- 
ever may be the vaporization produced. But now, 
if we suppose that the fire retains in all cases a 
constant intensity, capable of communicating per 
minute to 1 cubic inch of water a quantity of heat 
expressed by 1170 degrees of Fahrenheit, or 650 
degrees centigrade, we see that the boiler will be 
enabled to change 1 cubic inch of water into steam 
every minute, and that the cubic inch, thus trans- 
formed, will assume, according to the weight of the 
valve, 159>s., or 31 fts., or 48 lbs., or, in fine, 
65 fi>s. per square inch. And each of these effects 
will be produced without it being necessary to sup- 
pose that the fire has acquired any more intensity, 
that is to say, without any more fuel being con- 
sumed in one case than in the other. 

Thus it is seen that the vaporization resulting 
from a given consumption of fuel must always be 
sensibly the same, under whatever degree the steam 
in the boiler be generated. This, in fact, is con- 

s 



258 CHAPTER X. 

firmed by the experiments we have just presented. 
A slight advantage even is perceptible in those 
engines which work at higher pressure ; for the 
Goliath II. , working under the atmospheric pres- 
sure, vaporized on an average '036 cubic foot of 
water per hour and per square foot of heating sur- 
face ; and the Firefly II., under the effective pres- 
sure of 50 lbs. per square inch, instead of producing 
less, vaporized per hour and per square foot of 
heating surface, a quantity of water which amounted 
to '037 cubic foot. The other examples offer similar 
results. For instance, in the two experiments V. 
and VI., the Star, with the same blast-pipe and 
very nearly the same velocity, vaporized a greater 
quantity of water per hour under the pressure of 
45 lbs. per square inch, than under that of 38*7; 
and we find the same result in the experiments 
XXI. and XXQ. made with the engine Atlas. 

Considering the vaporization independently of 
the consumption of fuel, that is to say, seeking 
merely the quantity of water which the engines can 
vaporize per hour, without regard to the corre- 
sponding expenditure of fuel, we ought not to be 
surprised to find in general that the engines which 
work at a higher pressure produce a greater vapor- 
ization per hour. The reason is, that when the 
safety-valve of an engine is fixed, for instance, at 
50 lbs. of eflfective pressure per square inch, it is 
less liable to blow, that is, to let the steam escape, 
than when it is fixed only at 40 lbs. of eflfective 



OF THE VAPORIZATION OF THE ENGINES. 259 

pressure per square inch. In the latter case, then, 
the engine-man will see the valve blow more fre- 
quently, and this being for him a sign that his fire 
is as lively as need be, he will not serve the fire-box 
with the same activity; the result will be that he 
will indeed consume less fiiel, but he will produce 
less vaporization per hour in the engine. 

Thus, to recapitulate, we see that the vaporiza- 
tion in the engines is independent of the pressure 
in the boiler, and that even, when the vaporization 
is considered without regard to the corresponding 
expenditure of fuel, it is in general found more 
considerable under a high pressure than under a 
low one. 



Sect. III. Of the influence of the velocity of the 
engine on the vaporization of the boiler. 

It has been seen (Chapter VII.) that the pressure 
in the blast-pipe varies in the direct ratio of the 
velocity of the motion, and in the inverse ratio of 
the area of the blast-pipe. On the other hand, it is 
known that the draught which takes place in the 
fire-box is the result of the velocity assumed by the 
steam in the blast-pipe, and, consequently, in the 
chimney by reason of that pressure. It is natural 
then to think that the velocity of the engine and 
the size of the orifice of the blast-pipe must have an 
influence more or less considerable on the vapor- 
ization produced in the boiler. 



260 



CHAPTER X. 



In effect, on perusing the experiments which we 
have just presented, the influence of the velocity on 
the vaporization plainly appears ; for, collecting the 
experiments made on the same engine and with the 
same blast-pipe, but with a different velocity, we 
form the following Table. 



Experiments on the influence of the vehcUy of the engines 
on the vaporization of their boiler. 



Number 

of the 

expoiment. 


Name of 
the engine. 


Aram of the 
blast-pipe. 


Velocitj, 

in milea per 

hour. 


Vaporisation 
p«r hour. 


State of Uie water 
in the tender. 


{Ji. 


Star. 


sq. in. 
3-13 


miles. 
14-45 
1513 


cubic feet. 
68-79 
67-71 


Very hot 

Almost cold. 


lix. 


Star. 


6-25 


17-35 
18-32 


60-64 
61-05 


Hot. 
Lukewann. 


r xiii. 
txiv. 


FiesfltI. 


3-98 


17-70 
21-33 


6410 
77-31 


Almost cold. 
Lukewarm. 


rxv. 

1 XVI. 


FURT. 


3-65 


18-63 
19-67 


57-46 
54-45 


Cold. 
Cold. 


rxvii. 

t XVIIL 


Lbbos. 


3-65 


18-63 
21-99 


63-18 
68-82 


Scarcely tepid. 
Very hot. 


rxx. 

^XXI. 

[xxii. 


Atlas. 


6-78 
7-37 
6-78 


8-99 
15-00 
15-53 


43-81 
5000 
48-21 


Cold. 
Cold. 

Cold. 

1 



Comparing together those of the above experi- 
ments which were made with the same orifice of 
blast-pipe, and which we have, for that reason, 
united with a bracket, it appears that with the 
exception of the experiments V. and VI., XV. and 
XVI., in which, however, the change of velocity 
was quite inconsiderable, increase of velocity was 



OF THE VAPORIZATION OF THE ENGINES. 261 

invariably attended with increase of vaporization; 
but the extent of that increase seems to have been 
modified by the temperature of the water in the 
tender. Thus in the experiments XIII . and XIV., 
as well as in the experiments XVII. and XVIIL, 
the circumstance of the heat of the water in the 
tender has co-operated with that of the velocity 
to increase the vaporization, in the same manner 
as in the experiments V. and VI. that circumstance 
seems to have more than counterbalanced the then 
contrary effect of the velocity. It is only therefore 
by comparing together the experiments made with 
the engine Atlas, that we can form a tolerably 
exact notion of the influence of the velocity on the 
vaporization. In effect, in the three experiments 
made with that engine, the heat of the water in the 
tender was the same ; the blast-pipe had not per- 
ceptibly varied, and, with respect to the velocity, 
there was difference enough to give room to hope 
that other accessory circumstances would not be of 
weight sufficient to counterbalance its effect. The 
first of these experiments might then be compared 
to a mean taken between the two others ; but as in 
the third, the safety-valve of the engine was de- 
signedly fixed at a very low pressure, viz., 30fts. 
per square inch instead of 50, and as that circum- 
stance, by making the valve blow too easily, occa- 
sioned the engine-man not to keep up his fire with 
the same intensity as in the other experiments, we 



262 CHAPTER X. 

shall have a more exact result hy comparing only 
the experiments XX. and XXI. 

Now, in the first, the engine, at the velocity of 
8'99 miles per hour, vaporized 43'81 cubic feet of 
water, or * 1 72 cubic foot per square foot of heating 
surface ; and in the second, the same engine, at the 
velocity of 15 miles per hour, vaporized SO'OO cubic 
feet of water, or ' 1 97 cubic foot per square foot of 
heating surface. These numbers are almost in the 
precise ratio of the fourth roots of the velocities* 
We may therefore conclude that the vaporization, 
in locomotive engines, varies very nearly in the 
ratio of the fourth root of the velocity of their 
motion. 

This variation is, as we see, of slight importance 
in the most ordinary cases; but when very great 
difierences of velocity are concerned, like those, for 
instance, which take place in ascending inclined 
planes, where the velocity is often reduced to the 
half or the third of what it is on an average during 
the rest of the trip, we perceive that it then acquires 
a considerable influence, and consequently must not 
be omitted in the calculation. We shall take ac- 
count of this efiect in all the examples to be treated 
of in the sequel ; but it is easy to see, at the same 
time, that in a great number of practical applica- 
tions it may be dispensed with. 



OF THE VAPORIZATION OF THE ENGINES. 263 

Sect. IV. Of the influence of the orifice of the blasts 
pipe on the vaporization of locomotive engines. 

If attention be now directed to the effects of the 
blast-pipe, with reference to the vaporization, and 
if, with this view, the first series of the experiments 
already presented, in which no blast-pipe was used, 
be compared to the other series, in which, on the 
contrary, use was made of a blast-pipe more or less 
reduced in size, it will at once be observed that the 
application of the waste steam to the urging of the 
fire produces a very important effect, and that it 
nearly quintuples the natural vaporization of the 
boiler. But seeking afterwards what modification 
that effect undergoes from the narrowing more or 
less of the blast-pipe, we do not observe a very 
marked result in that respect. 

Examining, for instance, the experiments made 
with the Star, in which the alterations in the orifice 
of the blast-pipe enable us to study its influence on 
the vaporization of the boiler, and referring, accord- 
ing to what has been said in the preceding section, 
the effects produced to the velocity of 20 miles per 
hour, we form the following Table. 



262 CHAPTER X. 

shall have a more exact result by comparing only 
the experiments XX. and XXI. 

Now, in the first, the engine, at the velocity of 
8*99 miles per hour, vaporized 43'81 cubic feet of 
water, or * 1 72 cubic foot per square foot of heating 
surface ; and in the second, the same engine, at the 
velocity of 15 miles per hour, vaporized 50*00 cubic 
feet of water, or ' 1 97 cubic foot per square foot of 
heating surface. These numbers are almost in the 
precise ratio of the fourth roots of the velocities* 
We may therefore conclude that the vaporization, 
in locomotive engines, varies very nearly in the 
ratio of the fourth root of the velocity of their 
motion. 

This variation is, as we see, of slight importance 
in the most ordinary cases; but when very great 
differences of velocity are concerned, like those, for 
instance, which take place in ascending inclined 
planes, where the velocity is often reduced to the 
half or the third of what it is on an average during 
the rest of the trip, we perceive that it then acquires 
a considerable influence, and consequently must not 
be omitted in the calculation. We shall take ac« 
count of this effect in all the examples to be treated 
of in the sequel ; but it is easy to see, at the same 
time, that in a great number of practical applica- 
tions it may be dispensed with. 



OF THE VAPORIZATION OF THE ENGINES. 263 

Sect. IV. Of the influence of the orifice of the blasts 
pipe on the vaporization of locomotive engines. 

If attention be now directed to the effects of the 
blast-pipe, with reference to the vaporization, and 
if, with this view, the first series of the experiments 
already presented, in which no blast-pipe was used, 
be compared to the other series, in which, on the 
contrary, use was made of a blast-pipe more or less 
reduced in size, it will at once be observed that the 
application of the waste steam to the urging of the 
fire produces a very important effect, and that it 
nearly quintuples the natural vaporization of the 
boiler. But seeking afterwards what modification 
that effect undergoes from the narrowing more or 
less of the blast-pipe, we do not observe a very 
marked result in that respect. 

Examining, for instance, the experiments made 
with the Star, in which the alterations in the orifice 
of the blast-pipe enable us to study its influence on 
the vaporization of the boiler, and referring, accord- 
ing to what has been said in the preceding section, 
the effects produced to the velocity of 20 miles per 
hour, we form the following Table. 



264 



CHAPTER X. 



Experiments on the influence of the diameter of the blast- 
pipe on the vaporization of boilers. 



Number 

of the 

experiment. 


Area of the 
blast-pipe. 


Vaporization per sq. foot 

of total heating surface, 

at the velocity of 20 miles 

per hour. 


VIII. 
X. 

V. 
VI. 
IV. 
XI. 

VII. 
IX. 


sq. inches. 
1-25 
2-50 

313 
313 
3-75 
4-38 

6-25 
6-25 


cub. foot per hour. 
•227] 

;?^; Uo6 
•197J 

•190/ ^^" 



From these results, it appears that for this engine, 
of which the vaporization and heating surface have 
been given above, a blast-pipe of 3 to 4 square 
inches of area, or 2 to 2| inches in diameter, pro- 
duces an average vaporization of about '206 cubic 
foot of water per square inch of heating surface, per 
hour ; that the contracting of the blast-pipe within 
1*25 and 2*50 square inches, in nowise augments 
the vaporization, but even tends rather to diminish 
it ; and in fine, that the enlarging of the blast-pipe 
to 6*25 square inches, produces a slight diminution 
of from '206 to ' 1 90 cubic foot of water per square 
foot of heating* surface. 

These effects will easily be explained, from the 
considerations which we shall offer in the next 
section, on the comparative vaporization of the 



OF THE VAPORIZATION OF THE ENGINES. 265 

fire-box and the tubes of the boiler. It will then 
be at once perceived that, for a given surface of 
tubes^ there needs a certain draught, that is, a 
certain aperture of the blast-pipe, to carry the flame 
to the very extremity of the tubes, so that the 
whole of their extent may receive the direct action 
of the flame. This result once obtained, a greater 
contraction of the blast-pipe or stronger draught, 
could only have the effect of carrying the flame 
beyond the extremity of the tubes, that is, into the 
chimney, where it would no longer influence the 
quantity of water vaporized. Diminishing, then, 
the orifice of the blast-pipe still more and more, 
beyond this point, would produce no change at all 
in the vaporization of the boiler, if the extreme 
contraction of the blast-pipe would not render at last 
the passage of the air through the fire-box so rapid 
that the greater part of it traverse the fire without 
being used for the combustion. This is an eflfect 
which manifested itself in our experiments; for 
during those which took place with a blast-pipe 
of r25 square inch of area, every stroke of the 
piston caused in the chimney a violent noise, some- 
what resembling the report of a gun. It is readily 
conceived, then, that the contracting of the blast- 
pipe beyond certain limits, is productive of no ad- 
vantage to the vaporization of the engine. 

As to enlarging the blast-pipe too much, since 
it then ceases to supply a sufiicient draught in the 
fire-box to carry the flame to the extremity of the 



266 CHAPTER X. 

tubes, the remaining portion of these, beyond the 
point where the flame reaches, receives only the heat 
communicated by the contact of the hot gases re- 
sulting from the combustion already terminated; 
and the definitive vaporization must thereby be 
diminished. 

This latter case carried to the extreme, would at 
last considerably reduce the vaporization, and con- 
sequently the eflfect of the engines; and this in- 
deed is observed in practice, when a locomotive has 
been made with too large a blast-pipe, or when the 
latter has been corroded and widened by the effect 
of the fire ; but as these defects are easily recognised 
and corrected, they are to be regarded only as 
momentary and exceptional. Hence, in the calcu- 
lation of the effect of locomotives, we need consider 
but small variations in the diameter of the blast- 
pipe; and in such case, then, we see by the pre- 
ceding experiments, that the change resulting in the 
vaporization of the engine is not. of such importance 
as to require being introduced into the general 
formulae of the motion of these engines. 



Sect. V. Of the comparative vaporization of the 
fire-box and the iubeSy and of the definitive vapor- 
ization of the engines per unit of heating surface of 
their boiler. 

We have just inquired into the particular in- 
fluence, which divers circumstances may have on 



OF THE VAPORIZATION OF THE ENGINES. 267 

the vaporization of the engines : it now remains to 
examine the effects which may result in that respect 
from the construction of the boiler itself, or from 
the proportion that has been established between 
the heating surface of the fire-box and that of the 
tubes. We shall first seek then, how much of the 
total vaporization produced is attributable to each 
of these two portions of the boiler, and thence we 
shall afterwards conclude the definitive vaporization 
of the engines per unit of heating surface of their 
boiler. 

The boiler of locomotives consists, as we have 
seen, of two distinct portions, one of which sur- 
rounds the fire-box, the other contains the tubes. 
The water contained in the portion which surrounds 
the fire-box, is every where in contact either with 
the ignited fiiel, or with the flame which rises above 
that fuel. The water which surrounds the tubes, 
on the contrary, according to the intensity of the 
fire, and the length of the tubes, may be in con- 
tact, throughout the length of the tubes, either 
with the flame, that is to say, the ignited gases 
which issue from the fire-box, or partly with the 
flame and partly with the hot gases which are 
produced by the combustion. Now it is easy to 
conceive that the effect of the tubes will be very 
different in the two cases which we have just men- 
tioned. If the tubes are in contact with the flame 
throughout their length, it does not appear that, 
comparing equal surfaces, they ought to produce 



268 CHAPTER X. 

a vaporization less considerable than the fire-box ; 
for the ignited gases which traverse them, are 
fuel as well as the coke itself, and it may be said 
that throughout their length they receive the im- 
mediate and radiating action of the fire. But if the 
combustion slackens in the fire-box, so that the 
flame extend only half-way along the tubes, that 
portion alone of the tubes will be really submitted 
to the radiating action of the caloric, and the rest 
will receive no more than the communicative heat 
arising from the contact of the still hot gases re* 
maining after the combustion has ceased. Thus, in 
this case, the first half of the tubes may, with equal 
surface, produce as much vaporization as the fire- 
box, but the second half will necessarily produce a 
less effect, whence results that the mean vaporiza- 
tion of the tubes, per unit of their total surface, 
will then be less than that of the fire-box. 

In a series of experiments which we undertook in 
1836, at the station of the Liverpool and Man- 
chester Railway, with Mr. Edward Woods, the 
Company's engineer, on a boiler originally made 
for a locomotive, but used in a stationary engine, 
and in which the two compartments were separated 
by a partition, — a circumstance which admitted of 
measuring directly the vaporization produced by 
the fire-box and by the tubes, — we, in fact, obtained 
results analogous to those which have just been in- 
dicated. The boiler was very long, and when the 
fire was left to itself, and the vaporization not 



OF THE VAPORIZATION OF THE ENGINES. 269 

abundant, the tubes produced, comparing equal 
surfaces, an effect considerably less than the fire- 
box ; but by degrees, on the combustion being more 
excited, and especially when, by means of a blast- 
pipe taken from an adjacent boiler, a more violent 
jet of steam was applied to the urging of the fire, 
the effect of the tubes differed less and less from 
that of the fire-box. As these experiments have 
not been quite conclusive, we shall not report them 
here, as to the precise results ; but we mention the 
tendency of those results, in order to explain how, 
in an experiment on the same subject, an English 
engineer, operating on a small model, at rest, and 
without using the blast-pipe, could obtain for the 
proportion of the effect of the fire-box, to that of 
the tubes, the ratio of 3 to 1 ; and how, on the 
contrary, during the activity of the motion, with 
engines of the usual dimensions, and with the use 
of the blast-pipe, the two portions of the boiler may, 
if they are not too disproportionate one to the other, 
produce, per equal surface, equal effects, as we are 
about to see that it results from the preceding ex- 
periments, for the engines submitted to trial. 

Referring, in effect, to the Table of page 253, in 
which the engines are divided into series, according 
to the proportions existing between the fire-box and 
the tubes, we perceive that, in the first and second 
series, the total heating surface is about 6' 5 times 
that of the fire-box ; in the third series, it amounts 
to 8' 7 times that of the fire-box ; and in fine, in the 



270 CHAPTER X. 

fourth series, the total surface is but 4*5 times that 
of the fire-box. If then there were a considerable 
difference between the effect of the fire-box and that 
of the tubes, it would be found that in the engines 
wherein the fire-box forms a larger portion of the 
total sur£aboe, the eflect produced per unit of surface 
would be greater. But, on the contrary, if we ob- 
serve the means deduced fix)m the last three series, 
we find that notwithstanding the diversity of pro- 
portion between the fire-box and the tubes, the 
vaporization per square foot of total heating surface 
remains always sensibly the same. We must then 
conclude, that during the active working of engines 
of a construction similar to that of the experiments, 
the two portions of the boiler vaporize, per unit of 
surface, the same quantity of water. 

To know the vaporization of which a given engine 
is capable, it consequently suffices to measure the 
number of square feet composing its total heating 
surface, without distinction between the fire-box and 
the tubes, and then to multiply that number by the 
vaporization which each square foot of surface is 
capable of producing. It is then the latter quantity 
which we must now seek to determine ; but, as we 
have seen that the vaporization produced per unit 
of surface varies with the velocity of the motion, it 
is necessary to specify at the same time the velocity 
at which we wish to measure the vaporization. 

Now, referring to the experiments of page 253, 
we find that in the engines of the second series, the 



OF THE VAPORIZATION OF THE ENGINES. 271 



vaporization per square foot of heating surface was 
•198 cubic foot, at the velocity of 18* 15 miles per 
hour. On the other hand, we know that the va- 
porization varies in the direct ratio of the fourth 
roots of the velocities. We may then deduce from 
thence, that at the velocity of 20 miles per hour, 
the vaporization of those engines will be 

/ 20 \i 
• 198 V i815 / ~ '^^^ cubic foot of water per 

square foot of heating surface. 

Operating in the same manner for the two following 
series, we obtain, for the velocity of 20 miles per 
hour, the determinations of the following Table. 



Experiments on the vaporization of locomotive engines, per 
unit of total heating surface of their boiler. 



Nrnnber of 
the series. 


Average velo- 
city of the en- 
gine, in miles 
per hour. 


Vaporization per hour 

and per sq. foot of total 

heating surface, at the 

preceding velocity. 


Vaporization per hour 

and per sq. foot of total 

heating surface, at the 

velocity of 20 miles 

per hour. 




miles. 


cubic foot. 


cubic foot. 


2nd, 


1815 


•198 


•203 


3rd, 


2013 


•200 


•200 


4th, 


8-99 


•172 


•210 


4th, 


15-26 


•194 
Mean 


•208 


. . -205 



Thus, from these experiments, it appears that at 
the velocity of 20 miles per hour, the vaporization 



J 



272 CHAPTER X. 

of locomotives may be valued at 205, or, in round 
numbers, at '2 cubic foot of water per hour, per 
square foot of total heating surface of their boiler ; 
and it appears also that the different engines and 
different velocities lead to numbers almost identical, 
which tends to confirm the valuation we have just 
obtained. 

This determination is, as we have said, suitable to 
the velocity of 20 miles per hour ; but it is easy to 
deduce from it that which would take place at any 
other velocity, by multiplying by the fourth root of 
the ratio between the given velocity and the velocity 
of 20 miles. 

Such then will be the vaporization of an engine 
in motion, or, more properly, of an engine in which 
the blast -pipe is used. But if the engine is stopped, 
and the action of the blast-pipe interrupted in con- 
sequence, the first series of experiments presented 
page 253, proves that the vaporization per unit of 
heating surface then reduces itself, on an average, to 
•037 cubic foot of water per hour, that is to say, to 
about a fifth of what it is at the velocity of 15 or 20 
miles per hour. Thus, it will be possible, in all 
cases, to estimate the quantity of water reduced to 
steam by a given engine, in a determined time. 

It is to be remarked, that were the vaporization 
of engines considered as composed of two parts, 
namely, the vaporization at rest, which is constant, 
plus a variable augment depending on the velocity ; 
it would then be deduced from the preceding ex- 



L 



OF THE VAPORIZATION OF THE ENGINES. 273 

periments, that this variable portion changes in the 
ratio of the cubic roots, and not in that of the 
fourth roots of the velocities. But as, in reality, it 
is not the absence of velocity in the engine, but the 
interruption of the action of the blast-pipe, which 
produces the observed decrease of vaporization, 
during the moments of rest of the engines, it ap- 
pears more accurate to consider these two effects of 
the engine, with or without blast-pipe, as entirely 
distinct from each other. Thus we will say that 
the engine, at rest or in motion, but without blast- 
pipe, vaporizes about 037 cubic foot of cold water 
per hour, per square foot of total heating surface ; 
but that, the action of the blast-pipe once intro- 
duced and regulated by the velocity, the vaporization 
will vary according to the fourth root of the latter, 
and that at the velocity of 20 miles per hour, the 
vaporization will be '205 cubic foot of water per 
hoiu*, per square foot of total heating surface. 

It must however be observed, with respect to 
these determinations, that they are strictly suitable 
only to boilers constructed in proportions not very 
different from those used in the experiments ; that 
is to say, according to what has been explained 
above, that the heating surface of the fire-box ought 
not to be under a tenth of the total heating surface 
of the boiler, and the orifice of the blast-pipe not 
much larger than we had it in our experiments, 
according to the adopted practice. Were any 
notable change made in this respect, were the coke 

T 



\ 



274 CHAPTBR X. 

of an inferior quality, or the engine materially dif- 
ferent in construction fix)m what we have described, 
there would be grounds for a new determination 
of the vaporization. 

In fine, we will again add, that the numbers ob- 
tained above indicate rather the consumption of 
water of the boiler, than the real vaporization pro- 
duced ; for we shall presently see, that out of the 
total water thus expended by the engine, there is a 
portion which is drawn into the cylinders, mixed 
with the steam, but without being itself vaporized. 
Consequently, to obtain the real vaporization of the 
engine, it will be necessary to take account of this 
circumstance, as we shall do further on. 

Sect. VI. Of the loss of steam which takes place by 
the safety-valves^ during the work of locomotive 
engines. 

Among locomotive engines there are a great 
number which are subject to a continual loss of 
steam by the safety-valves. This effect arises from 
the engine being designedly constructed with an 
excess of power ; that is to say, that according to 
the production of steam which takes place in its 
boiler, the engine could draw its regular load at a 
greater velocity than it is allowed to do. The result 
is, that to prevent the engine from acquiring too 
great a velocity, it becomes necessary partially to 
close the regulator, that is, to diminish the passage 



1^ 



OF THE VAPORIZATION OF THE ENGINES. 275 

of the steam, till no more enters the cylinder than 
the quantity necessary to produce the desired ve- 
locity. Then the surplus accumulating in the boiler, 
at last raises the safety-valve and escapes into the 
atmosphere. When this loss takes place only on 
the regulator being somewhat closed, it is but a 
proof, as we have said, of a surplus of power which 
the engine holds in reserve. But if it takes place 
more or less under all circumstances, then it de- 
pends on the steam-ways being too narrow, and is 
consequently a defect in the engine ; in either case, 
however, it is necessary to obtain a valuation of 
this loss. 

There is yet another case in which engines are 
subject to a loss of steam by the valves ; but this 
loss is owing to a different cause fix)m the preceding, 
and exhibits itself much more abundantly: it is 
when the engine ascends a steep accUvity, with an 
apparently moderate load, or when it ascends a 
moderate inclination, with a very heavy load. At 
these moments the valves are always seen to emit 
an enormous quantity of steam. The reason is that, 
as soon as the engine reaches the inclined plane, its 
load instantly becomes extremely heavy, on account 
of the surplus of traction required by the gravity on 
the plane. It has been shown, in effect, that on a 
plane inclined iho^ every ton produces, by gravity 
alone, a resistance equal to that of 3*7 tons on a 
level. It happens therefore, at that moment, that 
the resistance of the train may become greater than 



i^ 



276 CHAPTER X. 

the actual pressure of the safety-valve. Conse- 
quently the steam, instead of flowing by the cylinder, 
driving back the piston, raises the safety-valve, and 
escapes into the atmosphere. If then the passage 
which the steam thus opens for itself were sufficient 
for its total efflux, no more steam would pass 
through the cylinder, and the engine would in- 
evitably stop. But we have already said, in speak- 
ing of safety-valves, that they are held in place by a 
spring which exerts a resistance by so much the 
greater as it is more compressed. The si^ety-valve 
then, being raised by the steam, acquires more and 
more pressure, and thus there will occur a point 
when that pressure becomes sufficient to keep the 
train in motion on the plane. The steam at this 
moment is free to escape at once by the safety-valve 
and by the cylinder, and divides itself between the 
two issues, in proportion to the orifices ofiered by 
them. Consequently the motion of the train then 
continues, but on condition that the steam shall 
preserve this accidental pressure ; that is to say, 
that the valve shall still remain at the same point 
of elevation, or in fine, on condition that a con- 
siderable portion of the steam shall be lost in the 
atmosphere. This loss might be greatly diminished, 
by momentarily increasing the pressure of the 
safety-valve, so as to put it in equilibrio with the 
resistance which the train on the inchned plane 
produces against the motion ; but as it might 
happen, if the engine-men were allowed this facility, 



i 



OF THE VAPORIZATION OF THE ENGINES. 277 

that they would use it inconsiderately and to the 
detriment of the engine, a collar is usually fixed 
on the rod of the spring-balance, which hinders the 
nut from being tightened beyond a certain point. 
This loss therefore is inevitable, whenever the de- 
finitive resistance produced by the train exceeds the 
extreme pressure thus fixed on the engine. 

We are now about to consider in turn the two 
wastes of steam of which we have just spoken. 

To obtain some estimation of the quantity of 
steam which escapes by the safety-valve, during 
the regular work of locomotives, we had recourse 
to the following method. During the whole con- 
tinuance of the experiments on vaporization, which 
we have just presented, we noted the point at which 
the valve began to rise, and carefully observed the 
mean point at which it stood by the effect of the 
blowing of the steam. The interval between these 
two degrees gave the rising of the valve during the 
experiment, a rising in virtue of which the issue of 
the steam took place. Thus it will presently be 
seen that in experiment XII., the valve of the 
Vesta, fixed at 20 degrees of the balance as the 
starting point, rose on an average to 21*3 degrees 
by the blowing of the steam. The rising of the 
valve, or the passage constantly opened to the 
steam, during the experiment, was therefore 1*3 
degrees measured on the balance. 

On the other hand, when the regulator of the 
engine was designedly closed, the whole of the 



278 CHAPTER X. 

Steam generated in the boiler was forced to escape 
by the safety-valve. Observing then how many 
d^rees the valve rose, we could recognise the 
nnmber of d^rees which corresponded to the total 
production of steam in the boiler. Comparing then 
the first rising with the second, that is to say, the 
partial opening of the valve, which took place in 
the regular work of the engine, with the opening 
capable of allowing the total issue of the steam, we 
could estimate the loss under consideration, as a 
portion of the total steam produced in the boiler. 

In the following Table we have collected the ob- 
servations made on this head, first during the expe-- 
riments on vaporization already given, and after- 
vrards while the r^ulator was totally closed. With 
respect to the number of d^rees which represent 
the total issue of the steam in difierait engines, it 
will be conceived that this number depends firstly 
on the quantity of steam produced by each boiler ; 
again, on the diameter of the valve, which, for a 
same degree of rising, may allow a greater or less 
passage to the steam; then on the dimensions of 
the levers and the size of the divisions of the 
balance, which make a d^ree of that balance cor- 
respond to a more or less considerable rising ; and 
lastly, on the state of the second safety-valve of the 
engine, which may itself give more or less issue to 
the steam, or may not give it issue at all. 



OF THE VAPORIZATION OF THE ENGINES. 279 



Experiments on the habitual waste of steam which takes 
place by the safety-valves of locomotive engines, during 
their regular work. 



Number 

of the 

experiment. 


Nttneofthe 
engine. 


Rising of the valve, 
in degrees of the 
balance, observed du- 
ring the experiment. 


Rishig of the valve, in de- 
grees of the balance, suf- 
ficient to give issue to the 
totality of the steam formed 
during the complete dose 
oif the regulator. 


XII. 


Vksta. 


1-3 


3-5 


XIII. 


FiRBFLT I. 





3 


XIV. 





•7 


3 


XV. 


Fury. 


1-5 


5 


XVI. 


— 


1-4 


5 


XVII. 


Lrxdb. 


1-2 


5 


XVIII. 


— 


20 


5 


XIX. 


Vulcan. 


1-5 


5 


XX. 


Atlas. 


•7 


4 


XXI. 


— 


•1 


4 


XXII. 




1-5 


4 


11-9 


46-5 



From this Table it is seen that the rising of the 
valve which took place in the experiments was, in 
degrees of the balances, 11*9 out of 46*5, that is to 
say, it amounted to nearly a fourth of the total 
steam produced during the total close of the regu- 
lator. Now, during the close of the regulator, the 
steam produced by the engine no longer passes to 
the cylinders, and consequently ceases to urge the 
fire in the fire*box ; and we have seen that during 



280 CHAPTER X. 

the suspension of that artificial excitation of the 
fire» the engine produces scarcely a fifth part of its 
vaporization during the work. It is therefore to be 
concluded from the preceding experiments, that in 
the engines submitted to observation, the loss of 
steam by the valves might be valued approxima- 
tively at ^ of the total steam produced in the 
boiler during the motion of the engine. 

The loss which has just occupied our attention is 
in some sort permanent during the work of the 
engines, and among all those which we have sub- 
mitted to experiment, the Star, whose passages for 
the circulation of the steam are very large, is the 
only one that was exempt from it. It will be ne- 
cessary then to take account of this circumstance, 
for all engines liable to it, during the whole con- 
tinuance of the work of the engine. 

As to the loss which now remains to treat of, and 
which is occasioned in ascending steep acclivities, it 
takes place in all engines; but it is merely acci- 
dental, and need not be taken into consideration 
except in calculations that may be relative to the 
traversing of those planes. To obtain an approxi- 
mate valuation of this loss, we used the same mode 
as in the preceding research: we attentively ob- 
served the engines of the Liverpool and Manchester 
Railway, while ascending, without an auxiliary en- 
gine, the planes of Sutton and WMstan, inclined ^ 
and ^, and the acclivity of Chatmoss, inclined iin^, 
and noted the jising of their valves which took 



OF THE VAPORIZATION OF THE ENGINES. 281 

place. The following Table contains the result of 
those observations, compared as before with the 
rising capable of giving issue to the whole of the 
steam produced in the boiler during the complete 
close of the regulator. 

Experiments on the (accidental loss which takes place by the 
safety-valves of locomotive engines ^ while ascending planes 
considerably inclined. 



Name of 
the engine. 


engine. 


Load of 
theenginct 

tender 
included. 


Inclina- 
tion of 

the 
plane. 


Velocity 

of the 

enjrine, in 

muea per 

hoar. 


Rising of the 
valve, in de- 
grees of the 
balance, ob- 
served during 
the ascent of 
the plane. 


Rising of the 

of the balance, 
sufficient to give 

issue to the to- 
talitv of the steam 
proauced during 
the complete close 
of the regulator. 


Vesta. 

Fu»Y. 

Fu»T. 

Lkkds. 

Vulcan. 

Atlas. 

Atlas. 


tons. 
8-71 

8-20 

8-20 

7-07 

8*34 

11-40 

11*40 


tons. 
33-15 

48-80 

56-16 

3515 

39-07 

195-5 

40-15 


tAtt 


miles. 
14-11 

15-00 

6-31 

10-00 

11-42 

8-00 

7-50 


2-50 

4 

3 

I 

5 

1-75 

2-50 


3-5 

5 

5 

5 

5 

4 

4 


19-75 


31-5 



From these experiments, it is visible that when, 
by reason of an excessive load on a moderate in- 
clination, or of an ordinary load on a steep acclivity, 
the engines are called upon to work at a pressure 
higher than that fixed by their safety-valve, they 
are liable to a variable loss, but which here on an 



282 CHAPTER X. 

by the boiler during the close of the regulator. And 
as we have shown that the latter vaporization is ^ 
of that which takes place during the action of the 
blast-pipe, that is, during the progression of the 
engine, the above loss may be represented by 

19-75 



31-5 



Xi = i=-12 



of the total vaporization produced by the engine 
during its motion. 

It is conceivable, however, that the extent of this 
accidental loss must vary under different circum- 
stances, and that it depends on the diameter of the 
valves, the length of the levers, the elasticity of the 
spring of the balance, and above all on the excess 
of the momentary resistance of the train above the 
pressure at which the safety-valve of the engine is 
regulated. For this reason, in calculations wherein 
precision is required, it will be necessary, as much 
as possible, to take account of it from direct ob- 
servation for every engine. 



Sect. VII. Of the water draivn into the cylinders 
in its liquid state^ and of the effective vaporization 
of the engines. 

There exists another loss much more important 
than the preceding, and to which locomotive engines 



OF THE VAPORIZATION OF THE ENGINES. 283 

are particularly gubject, by reason of the continual 
jerks which they undergo in their motion, of the 
little elevation of the entrance of the steam-pipe 
above the level of the water, of the small space 
reserved to the steam for its accumulation, and of 
the exceeding rapidity with which the steam issues 
from the liquid in the boiler. This loss consists of 
a considerable quantity of water drawn into the 
cylinders in its liquid state, and mixed with the 
steam, but without being itself vaporized. To con- 
ceive how this effect is produced, it suffices to 
observe the enormous quantities of water which are 
held in suspension in the air, in the form of douds, 
and borne about by the wind. As, moreover, the 
steam which is produced in the boiler of locomo- 
tives is of a density much greater than that of the 
air, and as instead of touching merely the surface 
of the liquid, it disengages itself from the very 
middle of that liquid, one need not be surprised 
that it draws along with it a very considerable mass 
of water ; and this effect will naturally be produced 
during the whole time of the work of the engine. 

To obtain a valuation of the loss which occurs in 
locomotives from this cause, we, either by aug- 
menting the load, or by lowering the pressure, or 
by choosing inclined portions of the road to tra- 
verse, placed the engines in such circumstances that 
the pressure of the steam in the cylinder could differ 
but very little from the pressure in the boiler i and 
we then compared the velocity really produced, with 



284 CHAPTER X. 

that which ought to have heen produced, had the 
totality of the water expended by the engine been 
really converted into steam. The difference between 
the water corresponding to the actual velocity of 
the engine and the total water expended during 
the motion, showed the quantity of water carried 
in its liquid state into the cylinders with the steam. 
The cases in which the engine works at a pressure 
in the cylinder sensibly equal to that of the boiler, 
have already been pointed out; they are those 
wherein the engine reduces its velocity till it be- 
comes impossible to admit that the steam can 
increase in volume, and consequently diminish in 
pressure on entering the cylinder, since such an 
increase of volume, slight as it might be imagined 
to be, would necessarily bring with it a greater 
velocity of the engine than the velocity observed. 
Now in performing for the different experiments 
which we are about to report, the calculation neces- 
sary to compare the real velocity of the engine with 
the velocity which ought to correspond to the total 
expenditure of water of the boiler, it will be recog- 
nised that in those experiments, the pressure of the 
steam in the cylinder could not be sensibly less than 
the pressure in the boiler ; and this fact will again 
be found verified on performing, in the manner 
developed in Chapter IX., the calculation of the 
resistance then exerted by the load against the 
piston, a resistance which we shall see equal to the 
pressure of the steam in the cylinder. 



OF THE VAPORIZATION OF THE ENGINES. 285 

To show how the calculation has been performed 
in the following experiments, we will give it in 
detail for the first of them. In this experiment, the 
engine Atlas, expending 43*81 cubic feet of water 
per hour, at the average velocity of 8*99 miles per 
hour, assumed on an inclined plane and with a 
considerable load, a velocity of 8*00 miles per hour, 
working at a total pressure of 69*7 fts. per square 
inch in the boiler. As the engine was then moving 
only at 8 miles per hour, whereas its mean vapor- 
ization of 43* 81 cubic feet of water had been 
observed at the velocity of 8*99 miles per hour, and 
as it has been shown that the vaporization of engines 
varies as the fourth roots of the velocities, we see, 

firstly, that its vaporization during the portion con- 

» 

sidered of the experiment, must have decreased to 
42*56 cubic feet. 

On the other hand, the safety-valve of the engine, 
observed at the same moment, was raised 1*75 
degrees of the balance, and in the engine Atlas, 
an elevation of 4 degrees of the balance suflices, as 
has been said above, to give issue to the whole of 
the steam that the engine can produce while at 
rest. The loss of steam by the safety-valve was 
therefore 

1^ = -4375 
4 

of the vaporization of the engine at rest. Now it 
has been shown that the vaporization while at rest 
is '037 cubic foot of water per hour, per square foot 



286 CHAPTER X. 

of total heating surface ; and referring to the Table, 
page 37, Chapter I., we see that the total heating 
surface of the Atlas is 254 '31 square feet. Hence 
the loss of steam which took place by the safety- 
valve during the ascent of the plane, was 

•4375 X 037 X 254-31 =4- 12 cubic feet per hour. 

Consequently the effective vaporization of the en- 
gine, at the same moment, was 

42-55 — 412 = 38-43 cubic feet per hour. 

But since the pressure in the boiler, at the moment 
of the experiment, was 69*7 fts. per square inch, 
and the relative volume of the steam at that pres- 
sure is 407 times that of the water, it is dear 
in the first place, that admitting the steam to have 
been expended in the cylinder at the pressure of the 
boiler, which is the greatest pressure it can be 
supposed to have, it would have produced a volume 
of 

407 X 38-43 =15641 cubic feet. 

On the other hand, as the diameter of the cylin- 
ders of this engine is 1 foot, and the stroke of the 
piston 16 inches or 1*33 foot, the two cylinders 
augmented by ^ for the vacant spaces filled by the 
steam at each stroke, but not traversed by the 
piston, offered a capacity of 

2-199 cubic feet. 

Such then was the volume of steam expended at 
each stroke of the piston. But since the engine 



OF THE VAPORIZATION OF THE ENGINES. 287 

moved at a velocity of 8 miles or 42240 feet per 
hour, with a wheel of 5 feet in diameter, '^r 15'71 feet 
in circumference, it follows that it performed in an 
hour 2689 turns of the wheel, and consequently 
gave 5378 strokes of the piston in both the cy- 
linders. The volume therefore of steam which it 
expended was but 

5378 X 2- 199 = 11827 cubic feet. 

Now, we have seen that supposing the steam to 
have had in the cyUnder the same pressure as in the 
boiler, it would already have produced a volume of 
15641 cubic feet, and every supposition of a smaller 
pressure for the steam carries with it the necessity 
of a volume still greater. Consequently, it is im- 
possible to admit that the steam can have expended 
itself in the cylinder at a lower pressure than in the 
boiler. 

Moreover, since, supposing even the steam in the 
cyUnder at the same pressure as in the boiler, which 
is the most favourable supposition we can make, it 
still happens that the volume of steam expended 
by the cylinder is less than the volume of steam 
generated in the boiler, a part of the water must 
have been carried from the boiler to the cylinder, in 
its liquid state; and the comparison between the 
quantity of water consumed by the boiler and that 
which, in the state of vapour, corresponds to the ve- 
locity of the piston, shows that the quantity of water 
really converted into steam, is to the total quantity 
of water consumed, in the ratio of the numbers 



288 CHAPTER X. 

15641 

Thus, in this experiment, we see that '24 of the 
water expended by the boiler was carried into the 
cylinders without being reduced to steam, or that the 
real vaporization of the engine was '76 of the total 
water expended. 

For the other experiments, we give in the fol- 
lowing Table all the elements of the calculation, 
which is performed in a manner entirely similar, 
except that in the experiments made with the engine 
Star, on the acclivity of r^o> ^^ blowing of the 
safety-valve took place, which dispenses with intro- 
ducing a reduction in that respect. 

It will be observed that if, in any one of these 
experiments, we had committed an error in admit- 
ting that the pressure in the cylinder was the same 
as in the boiler, it would then follow that the 
quantity of water carried in its liquid state with the 
steam, would have been greater than our determina- 
tion gives it, for that experiment. Consequently, 
we are siure that the result which we have obtained 
is not exaggerated. 

It will be remarked, again, that the loss here ob- 
served in the engines, cannot be attributed to the 
partial condensation of the steam in the steam-ways 
and cylinders, because the position of these in the 
smoke-box, where they are in continual contact 
with the flame of the fire-box, renders that supposi- 
tion quite inadmissible. 



OF THE VAPORIZATION OF THE ENGINES. 289 



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290 CHAPTER X. 

These results make known the quantity of water 
carried in its liquid state, with the steam, in the 
engines submitted to experiment. When we shall 
present (Chapter XII.) a series of obsenrations on 
the velocity and load of locomotives, it will appear 
that two experiments made with the engine Star, 
on the plane inclined g^, would equally have fur- 
nished, for that engine, a determination of the 
quantity of water carried with the steam ; but as, 
in these two cases, the risings of the valve took 
place without being observed, and as it could have 
been estimated only approximatively, we deemed it 
proper to prefer the two expmments of the Table, 
on the plane inclined nj^, because there was then 
no loss by the valve, which removed all error in this 
respect. 

Among the engines which we submitted to ex- 
periment, as will be seen further on, there are two, 
the Firefly and the Leeds, in which we have not 
been able to determine the quantity of water carried 
with the steam. The reason of this is, that the 
former being then in a bad state of repair, and 
losing water by the tubes, was never in a condition 
to work with a heavy load. As to the second, it 
once ascended the plane inclined ^ with a load of 
35' 15 tons, and must have worked at full pressure 
in the cylinder ; but as this engine, when its r^u- 
lator was quite open, was liable to prime consider- 
ably, that is, to fill its cylinders with water in a 
liquid state, and then to throw that water through 
the chinmey in the form of rain, it was never made 



OF THE VAPORIZATION OF THE ENGINES. 291 

to work but with the regulator partially closed. On 
the other hand, when ascending the plane inclined 
^ , the regulator had been entirely opened, in order 
not to impede the work of the engine. It was then 
found to lose a great deal more water than in the 
ordinary course of its work. This experiment, then, 
could only determine the quantity of water carried 
in a liquid state, in an exceptional case, and not in 
the regular working state of the engine. The other 
en^es not being liable to the effect we have just 
mentioned, did not offer the same difficulty. 

The results which have just been presented above 
show that the quantity of water carried away with 
the steam, varies in different engines, and ought to 
be determined for each separately ; but as, in taking 
the means between the different experiments, that 
loss is found to amount to '24 of the total vaporiza- 
tion of the boiler, this proportion may be adopted 
approximatively for engines that have not been 
directly submitted to experiment in this respect; 
that is to say, in order to have the effective vapor- 
ization of a locomotive, the total vaporization of 
which its boiler is capable, must be first measured ; 
from the result must be subtracted, if necessary, the 
loss, either accidental or permanent, which may be 
observed at the safety-valves, and the remainder 
must be multiplied by the fraction 76. Thus will 
be obtained the volume of water which passes into 
the cylinder, in the real state of steam, and produces 
the motion of the piston. 



292 CHAPTER X. 



average determination may serve for engines 
not submitted to the experiment, as the Leeds and 
the Firefly ; but for those which have been the ob- 
ject of a particular determination, the latter ought 
of course to be employed, because the quantity of 
water carried with the steam evidently depends on 
the peculiar construction of each engine, and espe- 
cially on the space reserved for the steam to form and 
accumulate in the boiler. If, in effect, that space is 
but ten times the capacity of the cylinder, it is clear 
that, at every stroke of the piston, a tenth of the 
steam generated will pass into the cylinder, and the 
density of the remaining steam will thus be found 
all at once reduced to nine-tenths of what it was 
before. This great change of density will immedi- 
ately demand from the liquid, a new quantity of 
steam to replace that which is gone ; but it is evi- 
dent that the new steam will emerge from the Uquid 
with so much the more violence, and consequently 
will draw by so much the more of that Uquid with 
it, as it shall rush into a more rarified medium. If 
then the space reserved to the steam in the boiler 
contain 100 cylinders-full of steam, instead of 10, 
as the difference of density produced at each stroke 
of the piston will be but y^, instead of |^, the 
quantity of water carried away with the steam will 
be by so much less considerable. This is a fact well 
known in practice; for engines are observed to be 
much more liable to prime when the boiler is full, 
than when it is moderately filled. In locomotive 



OF THB VAPORIZATION OF THB ENGINES. 293 

engines, the space left to the steam for its formation, 
consists of the top part of the boiler, and what is 
called the steam-dome. Clearly then, a boiler too 
small, or a steam-dome too confined, tends to aug- 
ment the effect under consideration. 

Moreover, if the entrance of the steam-pipe is 
but little elevated above the surface of the water 
of the boiler, and if it has a large diameter, the 
result must naturally be, that the steam will the 
more easily be raised to the entrance of the pipe, 
and be received into it in greater abundance. This 
is why some engines are subject to priming when 
their regulator is quite open, which depends on the 
orifice of the regulator ; and were the inquiry as to 
the quantity of water carried with the steam sus- 
ceptible of sufiicient precision, it is probable that in 
all engines that quantity would be found somewhat 
greater in the cases wherein the regulator is entirely 
open, than in those wherein it is but partially so. 

The quantity of water carried with the steam 
must then vary according to the peculiar construc- 
tion of the engines ; but it is yet again influenced 
by circumstances independent of the construction. 
Thus, when a very active fire is made in the fire- 
box, as there is then produced in the boiler a very 
considerable vaporization for the quantity of water 
it contains, and as, in consequence, there results a 
current of steam, through the liquid, by so much 
the more violent, it is conceivable that the water 



294 CHAPTSR X. 

carried with the steam must augment at the same 
time. In like manner, fouhiess of the water, form- 
ing at the surfiBU^ a scum which the steam blows 
and traverses continually, must produce a similar 
effect ; and, in fine, the higher the pressure in the 
boiler, the more easily the steam must carry the 
liquid water with it. 

From what has just been seen, the carrying away 
of water in a liquid state takes place in the engines 
without any external sign of it being manifested, 
because the water mixed with the steam dissipates 
itself with it in the air. But there are moments 
when this effect is so violent, that it exhibits itself 
externally in a very evident manner. This occurs 
when the boiler is too full, or when, in order to set 
the engine in motion, the regulator is opened sud- 
denly, instead of being opened by degrees. At such 
times is seen inmiediately to fall from the chinmey 
an actual rain, which in practice is expressed by 
saying that the engine is priming. In the first case, 
the quantity of water carried with the steam evi- 
dently proceeds from the diminution of the space 
left to the steam for its formation. In the second, 
it proceeds from the opening of the regulator giving 
all at once a considerable issue to the steam, whilst 
the cylinders and pipes are then but sUghtly warm, 
and filled with a steam extremely rarified. The 
steam at that moment accumulated in the boiler 
is therefore in a manner carried off suddenly, and 



OF THB VAPORIZATION OF THB ENGINES. 295 

in the agitation caused by the rapid formation of 
the new steam, a great quantity of water is carried 
with it. 

The extent of the loss which, has just occupied 
our attention, explains how some boilers expend 
water so rapidly that it is impossible to keep them 
fiilly even at a very moderate velocity, and how it 
has sometimes happened that by merely changing 
the steam-dome of an engine, a considerable re- 
duction has been made in its expenditure of fuel. 
For this reason there is room to think that as the 
construction of locomotives shall advance towards 
perfection, this loss will diminish, and consequently 
the consumption of fuel which attends it will di- 
minish at the same time. It is however to be 
observed, that the loss of fuel resulting from this 
defect is not in proportion to the loss of water 
itself; because the latter being carried off from the 
boiler in a state of liquid, carries with it only the 
sensible beat indicated by the temperature of the 
boiler, whereas, the rest of the water being carried 
off in the state of steam, carries with it, besides, the 
latent heat necessary to its existence in the state of 
an elastic fluid. 



CHAPTER XL 



OF FUEL. 



Sect. I. Experiments on the consumption of fuel ne- 
cessary to produce^ in locom4)tive engines, a given 
vaporization. 

Bkfore passing on to the calculation of the effects 
of locomotives, there is still another element of that 
calculation which it is indispensable to consider; 
namely, the quantity of fuel necessary to produce, 
in locomotive engines, a given vaporization. 

In order to arrive at the determination of this 
element, during the experiments presented above, 
and which had for their object to make known the 
vaporization of the boiler, we carefully noted also 
the corresponding quantity of fuel consumed. To 
that end, the tender was first completely emptied of 
all the remaining fuel, the coke then accurately 
weighed and put into the tender. The fire-box 
was besides filled with coke to the level of the lower 
part of the door. At the end of the experiment, 
the fire-box was filled anew to the same height, and 
what coke remained in the tender was weighed with 
the same care as before starting. 

In all the experiments the fuel employed was 



OF FUEL. 297 

coke of the best quality, or Worsley coke, which 
is prepared expressly for foundries. When the 
engines use that which is obtained from the gas- 
works, they consume about 12 per cent, more, ex- 
clusively of the loss arising from the friability of 
that fuel. It has moreover been found that the 
sulphurous parts contained in it are particularly de- 
structive to metals, and for that reason the Liver- 
pool and Manchester Railway Company have com- 
pletely renounced the use of it, notwithstanding its 
moderate price. The smoke emitted by the com- 
bustion of coal prevents its being usually employed 
in locomotives, and therefore we have made no re- 
searches as to the use of that fuel. 

The experiments of which we are about to give 
the results were made on the Manchester and Liver- 
pool Railway. To take account of the delays which 
occurred on the road during the trip, and of the de- 
scent of the inclined planes with the regulator shut, 
we employed the same method as for the vaporiza- 
tion. That is to say, since experience shows that 
the consumption of fuel in the engines, while at rest 
or without the action of the blast-pipe, is about the 
fifth of their consumption while in motion, we have 
replaced the time of suspension of the action of the 
blast-pipe by the fifth of that time, which we have 
then added to the time of the effective progression 
of the engine ; and it is by the total time thus found 
that we have divided the fuel expended, to deduce 
therefrom the consumption of fuel per hour qf 
motion. 



298 



CHAPTER XI. 









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OF FUEL. 299 

In examining these experiments, it will be proper 
first to distinguish the efiects of the introduction of 
the blast-pipe itself, .from the effects which are 
afterwards due to the more or less contraction of it. 

The first three experiments, which were made 
without the application of the blast-pipe, prove that 
the fuel consumed per hour in a locomotive engme 
in which the waste steam is not employed to excite 
the fire, and consequently in a locomotive engine at 
rest, is but about a fifth of the consumption which 
takes place in the same engine, during the use of the 
blast-pipe, or during the progression of the train. 
This is the fact which we have just made use of to 
take account of the stoppages of the engines. 

As soon as the blast-pipe is employed, the con-, 
sumption of fuel per hour in the fire-box augments 
considerably, and consequently the corresponding 
vaporization. But comparing the first and second 
series of the preceding experiments, we perceive 
that the vaporization produced does not augment 
quite so fast as the consumption of fuel. In effect, 
in the second series, the ratio between the surface 
of the fire-box and the total heating surface ia 
nearly the same as in the first series. There is 
room then to think, from what will presently be 
seen, that the consumption of fuel per cubic foot of 
water vaporized, would have been nearly the same 
in the two series, if the second had not taken place 
with the use of the blast-pipe. Whereas, we find 
that the consumption of fuel, which was only 9 9>s. 



300 CHAPTER XT. 

of coke per cubic foot of water iu the first case, 
amounted in the second to ITSfts. Hence we 
must then conclude that the introduction of the 
blast-pipe greatly aids the combustion, but that the 
definitive vaporization produced by the engine does 
not augment in an equal proportion ; and we shall 
presently see the reason of it, viz., that when the 
consumption of fuel mcreases by the introduction 
of the blast-pipe, the heating surfieu^, remaining the 
same, no longer preserves the same proportion with 
the quantity of fuel consumed. 

Thus, at first, we see that the introduction of the 
blast-pipe leads to the result of increasing the con- 
sumption of fuel per hour in the fire-box, and 
likewise the vaporization of the boiler, though in a 
less proportion. But in seeking afterwards the in- 
fluence of a greater or less contraction of the blast- 
pipe, we cannot clearly distinguish any very marked 
effects in that respect. There is room to think 
that the consumption of fuel per hour, at equal 
velocities of the engine, must be increased to a 
certain degree by the contraction of the blast-pipe, 
as we have said in treating of the vaporization; 
but this augmentation appears too slight to show 
itself in a decided manner. It is easily found com- 
pensated by accidental circumstances, of which it is 
impossible accurately to take account, such as the 
quality of the fuel employed and the care of the 
engine-man in stoking the fire ; and we see defini- 
tively that, in practice, and regarding only the usual 



OF FUEL. 301 



variations of the blast-pipe, we may consider the 
consumption of fuel per hour as undergoing no 
sensible change with the size of the blast-pipe. 



Sect. II. Of the most advantageous proportion to 
establish between the fire-box and the tubes of the 
boiler^ in locomotive engines. 

It is still to be remarked in the preceding Table, 
that the diiferent engmes are more or less econo- 
mical with regard to fiiel, in proportion to the 
corresponding vaporization ; that is to say, they do 
not all consume the same quantity of fuel to pro- 
duce the same vaporization. With this in view, we 
have divided the engines into several series, accord- 
ing to the ratio which exists in each of them between 
the heating surface of the fire-box and that of the 
tubes, or, which comes to the same, between the 
heating surface of the fire-box and the total heating 
surface of the boiler. In the engines of the first 
and second series, the total heating surface is about 
6 '5 times that of the fire-box ; in the third series, it 
amounts to 8*7 times that of the fire-box ; and in 
fine, in the fourth series, the total heating surface is 
but 4*5 times that of the fire-box. The means 
deduced from each series of experiments show the 
motive of this division ; for, comparing them to- 
gether, we form the following Table. 



302 



CHAPTER XI. 



Experiments on the most advantageous proportion to be 
established between the fire-box and tubes, in locomotive 
engines. 



Nnmhcr 
of the 

•erica. 


Average heetuiK sur&ce 


Vaporisa- 

tionper 

hour. 


Cokeeon- 

samedper 

hour. 


Ratio between 
the total heating 
■urfkce, and that 

of the fire-box. 


Coke per 
cubktoot 

of water 
vaporised. 


of the 
fire-box. 


dfthe 
tube*. 


IV. 
II. 
III. 


Bq. feet. 
57-07 

49-30 

36-74 


sq. feet. 
197-25 

272-15 

282-09 


cub. feet. 
47-34 

63-47 

63-70 


lbs. 

551 

715 

583 


4-46 
6-52 
8-68 


!b8. 
11-65 

11-31 

918 



We see by this Table that the consumption of 
Aiel per cubic foot of water vaporized, is so much 
the less as the total heating surface offers a greater 
extent relatively to the fire-box ; and this result is 
easily accounted for on observing that the less fuel 
is consumed in an engine whose heating surface 
does not vary, the more heating surface there is 
per pound of fuel consumed, and consequently the 
more completely absorbed by the liquid is the ca- 
loric developed by each pound of fuel. Thus, in 
the third series, the fire-box was of such dimensions, 
that the engine consumed only 583 9>s. of coke per 
hour, whereas in the engines of the second series, 
the fire-box could consume 715 lbs. of coke in the 
same time. On the other hand, in each of the two 
series the total heating surface offered to the action 
of the fire was nearly the same, namely, 320 and 
321 square feet. The caloric developed by each 



OF FUEL. 303 

pound of coke was then received by a surface of 
f5J.==.45 square foot in the second series, and of 
f|^= -55 square foot in the third ; which explains 
the advantage of the latter on the score of economy. 
It is for the same reason likewise, that, in the first 
series, the engines without blast-pipe, though of 
similar proportions to those of the second series, 
have yet been more economical in their expen- 
diture, because the absence of the blast-pipe having 
rendered the consumption of fuel, in those engines, 
less considerable for a like heating surface, the case 
became similar to that of the third series compared 
to the second. 

Finally, a like effect is again recognisable in the 
comparison of the third and fourth series. In the 
latter, the quantity of fuel consumed was not greater 
than in the third series ; . but the heating surface 
exposed to receive the action of the fuel was only 
254 square feet instead of 320 ; and a corre- 
spondent difference of economy has resulted for the 
production of the steam. 

We may then at once conclude from what pre- 
cedes, that the most economical locomotive engines 
are those whose heating surface is the greatest rela- 
tively to the consumption of fuel in the fire-box ; 
and as, in the same system of construction of fire- 
boxes, and with the use of the blast-pipe, the con- 
sumption of fuel, that is, the capacity of the fire- 
box, may be regarded as sensibly proportional to its 
heating surface, it is visible that the most eco- 



304 CHAPTER XI. 

Domical locomotive engines, with respect to fuel, are 
those in which the total heating surface is greatest 
relatively to that of the fire-hox. 

From this remark, one should then be induced to 
increase more and mcHe the surface of the tubes 
relatively to that of the fire-box ; there would, in 
effect, be thus obtained a still greater and greater 
economy of fuel : but there is another condition yet 
more important in the use of locomotive engines 
than the saving of fuel ; and that is, to produce the 
greatest possible quantity of steam with a boiler of a 
given size. Now, it is evident that by more and 
more augmenting the surfece of the tubes, we should 
bring them at last to such an extent that the flame 
of the fuel could cover only a portion of them. 
Hence, from what has been said (Chapter X.), the 
vaporization of the boiler, per unit of heating surface 
would lower at the same time. 

This, in fact, is what is observed on the Great 
Western Railway. There are engines, on that line, 
in which the total heating surface is equal to 10*3 
times that of the fire-box, and others in which the 
ratio between those two surfaces is carried so fiBu: as 
11 '3 and 11*6. In the first, the consumption of 
coke is 8'801bs., and in the second, 8*43 lbs. per 
cubic foot of water vaporized. But at the same 
time, the vaporization of the first, referred to the 
velocity of 20 miles per hour, is '200 cubic foot of 
water per square foot of heating surface, as in the 
engines of the Table which we have presented 



OF FUEL. 305 

above, whereas in the second, the vaporization, re- 
ferred to the same velocity, is no more than '185 
cubic foot of water per square foot of total heating 
surface. It is clear then that, in the latter, the 
saving of fuel is obtained only at the expense of the 
effect of the engine, whereas with the proportion of 
about 10*3 between the total heating surface and 
that of the fire-box, the expenditure of fiiel is di- 
minished, without the definitive vaporization of the 
engine undergoing any reduction. 

These different effects are easily accounted for by 
the observations we have already made in treating 
of the vaporization ; but we will dwell yet a moment 
on the subject, to endeavour to recognise what is the 
most advantageous proportion to establish between 
the heating surface of the tubes and that of the fire- 
box. 

When the surface of the tubes amounts to but 
about 3 or 4 times that of the fire-box, as in the 
engines of the fourth series of our experiments, the 
engine consumed as much as ir65fts. of coke per 
cubic foot of water vaporized, because the excess of 
coke burnt in the fire-box serves only to carry the 
flame beyond the extremity of the tubes, that is to 
say, into the chimney, where it ceases to influence 
the vaporization, and can produce no other effect 
but to destroy rapidly the parts of the engine with 
which it comes in contact. Increasing then the 
surface of the tubes to 8 or 9 times that of the 
fire-box, as in the engines of the third series, the 

x 



306 CHAPTER XI. 

consumption of coke is reduced to 9'18!bs. of coke 
per cubic foot of water vaporized, without the de- 
finitive vaporization of the engine being affected, 
because the change has done no more than remedy 
the loss of fuel above mentioned. Finally, by aug- 
menting the surface of the tubes beyond 10 times 
that of the fire-box, a further reduction is obtained 
in the expenditure of fuel per cubic foot of water va- 
porized ; because not content with employing merely 
the flame which rises from the fire-box, we turn 
to use also a part of the caloric carried with the 
gases resulting from the combustion effected. But 
the portion of the tubes which serves to utilize this 
latter portion of caloric, produces much less vapor- 
ization than the rest of the boiler, whence results 
that the definitive vaporization of the engine, per 
unit of total heating surface, is found reduced at the 
same time. 

We have reason then to think, firom the difierent 
experiments cited above, that with coke for fuel, 
and with the other circumstances of the work and 
the construction of the engines, the most advan- 
tageous ratio to estabUsh between the total heating 
surface and that of the fire-box, would be nearly that 
of 10 to 1 : since for a less proportion there would be 
increase in the expenditure of fuel, without increase 
of vaporization; and for a greater proportion, on 
the contrary, there would be reduction in the 
vaporization of the engine per unit of surface, 
which would incur the necessity of a larger boiler, 



OF FUEL. 307 

and consequently of a greater weight, which it is 
important to avoid. 

In fine, to arrive at a general conclusion from the 
experiments which we have presented above, it ap- 
pears that, according to the proportion of the fire- 
box to the total heating surface, the consumption of 
fuel in locomotive engines varies from 92 to 11*3 
and 11*7 lbs. per cubic foot of total water vaporized ; 
so that it may, on an average, be valued at 

10'7fts. of coke, per cubic foot of total 
vaporization. 

Sect. II. Of the consumption of fuel necessary to 
draw a given load a given distance. 

The result which we have just obtained makes 
known the average quantity of coke consumed, in 
the engines submitted to experiment, to produce a 
determined vaporization ; but what is necessary to 
be known, in practice, is the quantity of fuel neces- 
sary to draw 1 ton a mile. Specif)dng in each of 
the experiments above noticed, and in some others 
which we are about to add to them, the load then 
drawn by the engine, and taking account of the dis- 
tance which that load was conveyed, we form the 
following Table, in which is seen the consumption 
of coke per ton per mile, which took place in each 
case. 

In this Table we first give the weight of the load, 
the duration of the trip, and the delays which oc- 



308 CHAPTKR XI. 

corred on the road ; and as the liyerpool and Man- 
chester Railway, on whidi the experiments were 
made, has, in each direction, besides divers less 
important acclivities, an indined plane on which 
it is often necessary to have assisting engines, we 
give also the number of those engines which were 
employed to draw the trains to the top of the 
planes inclined ^ and ^. We afterwards give 
the pressure of the steam in the boiler, and the 
velocity of the motion. The following column 
shows the consumption of coke which took place 
during the experiment, first such as it was ob- 
served, that is, delays included, and then delays 
deducted. To make this deduction, we proceed 
as it has been explained in the preceding section, 
that is to say, we add to the real duration of the 
trip the fifth of the delays, and by the time thus 
calculated we divide the total consumption of fuel, 
in order to obtain the consumption of coke which 
took place per hour or per minute, during the 
activity of the motion. Then, as soon as we know 
the consumption of ftiel per minute of active mo- 
tion, we take the fifth of it, which gives the con- 
sumption of ftiel of the engine per minute of rest ; 
after which it is easy to conclude that which takes 
place during the delays. Consequently, in fine, sub- 
tracting this from the total consumption, we obtain 
the numbers inserted in the eleventh column. 

From what has just been explained, we have all 
the elements of the experiments. Nothing remains 



OP FUEL. 309 

but to determine the quantity of work, in tons con- 
veyed 1 mile, which has been executed in each case ; 
and dividing the consumption of fuel, delays de- 
ducted, by the quantity of work done, we have the 
consumption of fuel per ton per mile, such as it 
is contained in the twelfth column. The following 
need no explanation. 

To obtain the quantity of work performed by the 
engine in each case, we refer the reader to Sect. vi. 
Chapter XVII. It will there be seen that, by reason 
of the different inclinations which exist on the Man- 
chester and Liverpool Railway, in order to obtain 
the quantity of work requisite for the draught of a 
train along the whole line, the following formulae 
must be used, according as the train is going from 
Liverpool to Manchester, or from Manchester to 
Liverpool, and according as the passage of the in- 
clined plane is performed with or without assisting 
engine : 

From Liverpool to f without assisting engine 30*79 M, + 206 
Manchester \ with assisting engine 30*79 M^ + 318 ; 

From Manchester f without assisting engine 36*89 M, + 292 
to Liverpool \ with assisting engine 36*89 M^ + 404. 

In these formulae, Mi expresses the load of the en- 
gine in tons gross, tender not included; and the 
constant number added to each expression, repre- 
sents the quantity of work consumed by the friction 
of the tender of the engine, and by the gravity of 
the engine and its tender, on the different acclivities 
of the line. In the case of assisting engines, the 



310 CHAPTBR XI. 

constant number comprises moreover an addition 
of 112 tons conveyed 1 mile, which represents the 
gravity of the assisting engine and its tender, and 
the friction of that tender itself, on the inclined 
plane traversed by the engine. 

These formulae gave then the total work per- 
formed by the trip engine and the assisting en- 
gine united, for the conveyance of the train upon 
the line. But if it be desired to know the work 
done by the trip engine, taken separately, then, 
from each of the foregoing expressions, must be 
subtracted the work done by the assisting engine. 
Now, as this engine is always more powerful than 
the trip engine, it may be estimated that, during 
the common action of the two engines, that is, 
during the passage of the inclined plane, the as- 
sisting engine, over and above its own weight and 
that of its tender, draws f of the load Mi. 

On the other hand, we have said that the weight 
of the assisting engine and its tender consumes, 
during the ascent of the plane, a quantity of work 
expressed by 1 1 2 tons conveyed 1 mile on a level ; 
and, recurring to Sect. vi. Chapter XVIL, it will be 
found that the ascent of the load M, on the inclined 
plane, causes, with regard to Ifriction and gravity, a 
quantity of work represented by 7*18 M, tons 1 
mile, f of which are 4*79 M| tons 1 mile. The 
total work performed by the assisting engine is 
therefore represented by 

479 M, + 112. 



OF FUEL. 311 

Finally then, subtracting, for the cases of assisting 
engines, this quantity from the preceding formulae, 
we have, for the quantity of work done by the trip 
engine, taken separately : 

From Liverpool to f without assisting engine 30" 79 M, -f 206 
Manchester \ with assisting engine 26*00 M , + 206 ; 

From Manchester f without assisting engine 36*89 M, -f 292 
to Liverpool \ with assisting engine 32*10 M^ -f 292. 

The result of these formulae gives, in tons gross 
conveyed 1 mile, the work executed by the engine 
during the total trip along the line. By this result 
then ought to be divided the quantity of coke con- 
sumed by the engine, delays deducted, to conclude 
the consumption of coke per ton conveyed 1 mile. 
Performing this calculation, we find the numbers of 
the thirteenth column of the Table. 



312 



CHAPTER XI. 



ExperimefUs on the quantity ofjwl consumed 



Number 
of theex- 
pcnuMut> 



VI. 
IV. 
V. 
VII. 
VIII. 
X. 
IX. 
XI. 

XXIII. 
XII. 

XXIV. 
XXV. 

XIV. 
XIII. 

XV. 
XVI. 

XVII. 
XVIII. 

XXVI. 
XIX 

XX 
XXVII. 

XXI. 
XXVIII. 

XXIX. 

XXX. 

XXXI. 
XXXII. 

XXII. 
XXXIII. 



Dftteofthe 

cxpenniMit. 



Aug. 9, 
Aug. 13, 
Aug. 9, 
Aug. 9, 
Aug. 11, 
Aug. 13, 
Aug. 11, 
Aug. 10, 

July 5, 
Aug. 1, 

July 16, 
July 16, 

July 26, 
July 26, 

July 24, 
July 24, 

Aug. 15, 
Aug. 15, 

July 1, 
July 22, 

July 23, 
July 9, 
Aug. 4, 
July 14, 
July 11, 
June 28, 
July 16, 
July 17, 
July 31, 
July 17, 



836. 
836. 
836. 
836. 
836. 
836. 
836. 
836. 

834. 
834. 

834. 
834. 

834. 
834. 

834. 
834. 

834. 
834. 

834. 
834. 

834. 
834. 
834. 
834. 
834. 
834. 
834. 
834. 
834. 
834. 



Name of the engUw, 
and place of ttarCing. 



Stab, from Uy. 

' from — 

— from Man. 

— from liv. 

from Man. 

' from — 

^— from LiY. 

' from — 

Vbsta, frt>m liT. 

— from Man. 

JupiTBE, from Man. 

— from Liv. 

FiRBFLT,from Man. 

— from liY. 

FnmT, from Man. 

-^— from liv. 

L»D8, frt>m LiY. 

—^ from Man. 

Vulcan, from liv. 

—^ from Man. 



Atlas, 



from Liv. 
from — 
from — 
fix)m -^ 
from — • 
from — 
from -^ 
frt>m — 
from Man. 
frx>m — 



Natnre and wdght 
of the load, in 

jitMay t ca da f 
not indiidad. 



23 wag. 
22vrag. 
35 wag. 
20 wag. 
15 wag. 
9 wag. 
12 wag. 
12 wag. 



tons. 

114*77 
104-18 
69-55 
90*80 
55-74 
42-98 
54-34 
38-15 



20 wag. 92-75 
10 wag. 28*15 

7 coach. 30-09 

8 coach. 33-09 

8 coach. 36-40 
8 coach. 36-40 

10 wag. 43-80 
10 wag. 51-16 

20 wag. 83-34 

8 wag. 32*01 

20 wag. 97-70 

9 coach. 34*07 



40 wag. 
25 wag. 
25 wag. 
25 wag. 
25 wag. 
25 wag. 
20 wag. 
15 wag. 

12 wag. 

13 wag. 



19000 

123-13 

122-64 

118-90 

117-61 

113-90 

94-66 

65*40 

35-15 

25-30 



Duiaticn ol 

the trip, 

delaya not 

indttdad. 



h. m. 



1 
2 
2 



57 
8 
15 
42 
41 
S4i 
37i 
25i 

42 

H 

12 

12 

18 
35 

35 
30 

35 
17* 

37 
17 

2 

48 
58 
31 
41 
50 
25 
27 
54 
26 



DelM* 
OB the 
mad. 



mm. 

15 
11 
3& 
36 
22 
5 

15* 
13 

5 


4 

3 

5 
5 





3 

3 
3 

15 
12 


19 

5 

5 
23 

3 



3 



Nnnber of 
aatistin^ 

lO 



theindined 
plaoei. 



1 
1 

1 
1 
1 
1 
1 

1 


1 
1 

1 
1 




1 


1 





2 
3 

(t 
ft 
2 
1 





OP FUBL. 



313 



by locomotive engines, in drawinff given loads. 





AvvfSfe 


Coke eoDsomed 


Coke 


Coke per 








Arerefe 


velocity 
of the 


during the trip, 


oon- 

siuned 

per hour, 


ton gross 
drawn cme 
mile one 


State ef the 
water in the ten- 






fffectiTe 






presrare 


in miles 


deUya 


delays 


deUys 


level, ten- 


der, at the 






in the 


PV 


ID- 


de. 


de- 


der not 


starting of the 


State of the 




boUer. 


Aoor. 


dnded. 


ducted. 


ducted. 


indoded. 


engine. 


weather. 


Obsenrationa. 


lbs. per 


miles. 


Its. 


Hw. 


Am. 


fbs. 








84). in. 


















38-7 


15-13 


1369 


1322 


708 


-41 


Almoat cold. 


Fair and calm. 




34-3 


13-85 


1431 


1398 


666 


•48 


Cold. 


Fair and calm. 


rss empty wag. 


45-1 


14-45 


1456 


1358 


652 


•54 


Very hot. 


Fair and calm. 


^ —The engine 

ascended the 

LplaneinStoms. 


35-8 


17-35 


1409 


1302 


805 


-51 


Hot. 


Fair and calm. 


?» 


17-46 


1248 


1182 


741 


-57 


Cold. 


Fair and calm. 


wag. empty. 


270 


18-79 


920 


900 


603 


•54 


Hot. 


Pair and calm. 




26-3 


18-32 


nil 


1064 


690 


•66 


Tepid. 


Fair and calm. 




23-5 


20-78 


1133 


1084 


809 


•90 


Hot. 


Fair and calm. 




53 


17-35 


916 


897 


555 


•34 


Hot. 


«Blm. 




51 


27-23 


774 


761 


761 


•57 


Very hot. 


Fkir, wind fav. 


S wag. empty. 


53 


24-58 


836 


812 


727 


•65 


f» 


Fair, wind agst. 




53 


24-58 


742 


721 


645 


•68 


Almost cold. 


Pair and calm. 




49 


21-33 


870 


847 


696 


•58 


Tepid. 


Rainy, wind agst 


/The engine in 
\ a bad state. 


44 


17-70 


879 


858 


639 


-75 


Almost cold. 


Fkir. 


57 


18-63 


746 


738 


492 


•39 


Cold. 


Fair, w. sideways. 




57 


19-67 


806 


797 


562 


•45 


Cold. 


Fair and calm. 




54 


18-63 


897 


887 


592 


•37 


Hardly tepid. 


Fair and calm. 


_ A ■ •« .a 


49 


21-99 


690 


675 


560 


•46 


Very hot. 


F^ and calm. 


/ 1 wag. half the 
iroad. 


54-5 


18-25 


1071 


1048 


684 


•38 


Tepid. 


Calm. 




54-5 


22*99 


664 


650 


541 


•42 


Hazdly tepid. 


Fair, wind agst. 




53-7 


8-99 


1596 


1561 


529 


•30 


Cold. 


Cahn. 




53 


16-39 


1102 


1071 


624 


•31 


Tepid. 


ff 


r Wheel con. 
necttng-rods 
. too tight. 


53 


15-00 


1224 


1213 


644 


•36 


Cold. 


Fair and calm. 


61-5 


19-45 


1118 


1057 


737 


-32 


Cold. 


Pair and calm. 


53 


17-53 


1136 


1113 


696 


•34 


Tepid. 


ft 




53 


1609 


1104 


1084 


619 


•34 


Rather hot. 


tt 




53-5 


20-82 


1081 


1005 


754 


•38 


Bather tepid. 


Calm. 




54 


20-35 


1012 


988 


723 


•52 


Very hot. 


Fair and calm. 




30 


15-53 


881 


873 


481 


•55 


Cold. 


It 


4 wag. empty. 


54-5 


20-58 


720 


703 


520 


-57 


Very hot. 


Pair and calm. 


8 wag. empty. 



314 CHAPTER XI. 

Examining these experiments, we immediately 
recognise that the quantity of coke necessary to 
draw a ton 1 mile, is so much the greater as the 
load of the engine is less, or as the velocity is 
greater. We recognise at the same time, that 
this effect is not owing to an increase in the con- 
sumption of fuel per hour ; for that consumption 
does not appear to undergo any regular change ; 
the variations we observe in it, sometimes in ex- 
cess, sometimes in diminution, being sufficiently 
explained by some accidental difference in the 
quality of the fuel, or in the assiduity of the 
engine-man in stoking the fire. But the difference 
noticed here is easily accounted for, on considering 
that the engine is obliged, besides its load, to draw 
its own weight and that of its tender, and to over- 
come divers constant resistances ; and the quantity 
of fuel necessary to perform this work being then 
divided according to the number of tons in the 
load, becomes by so much the more sensible as 
the load itself is lighter. Thus it is that we see 
the same engine expending twice and almost three 
times as much coke, per ton per mile, in one experi- 
ment as in another. 

It would therefore be inaccurate to draw an average 
result from the preceding Table, in order to apply 
it to the different cases that might occur. But if it 
be desired to know the quantity of fuel necessary 
for the engine per ton per mile, the load the engine 
is to draw must previously be given. Now, by 



OF FUEL. 315 

measuring the heating surface of the boiler, and 
recurring to the results obtained in Chapter X., the 
quantity of water which the engine is able to va- 
porize per hour will be known ; and consequently, 
from the experiments presented in Section i. of 
the present chapter, the corresponding consumption 
of fuel will be deduced. Then, by the formulae 
which will be developed in Chapter XIL, the ve- 
locity of the engine with the given load on any 
inclination whatever will be determined. There- 
fore, if the railway in question be level, or if it 
consist of one uniform inclination, in multiplying 
the given load by the velocity the engine will 
assume with that load, the product will immedi- 
ately make known, in tons conveyed 1 mile per 
hour, the useful effect of the engine. Dividing 
then the consumption of fuel of the engine per 
hour, by the useful effect produced in the same 
time, the quotient will give definitively the quantity 
of fuel which will be consumed by the engine, per 
ton per mile, in drawing the given load. This 
method will be a natural consequence of the very 
theory of the engine, as will be seen in Chapter 
XIL, when we come to treat of the useful effect 
of locomotive engines, and for this reason we shall 
not dwell any longer upon it here. 

If the railway in question, instead of being es- 
tablished on a uniform inclination, be composed 
of a series of ascents and descents, the velocity 
of the engine must be calculated on each of the 



316 CHAPTBR XI. 

inclinatioiis ; and, by the process indicated in Sect. 
III. Chapter XVII., the total time of the trip will 
be determined. Consequently, since the consump- 
tion of fuel per hour is already known, that which 
will take place during the whole duration of the trip 
will immediately be concluded. Then, proceeding, 
as we have just done, to form the foregoing Table, 
or as will be explained Sect. ti. Chapter XVII., 
the work executed by the engine during the same 
trip will be obtained. Dividing then the expendi- 
ture of fuel by the work executed, the result will 
definitiyely be the quantity of coke, per ton per 
mile, expended by the engine, in drawing the given 
load, on the variously inclined railway in question. 



CHAPTER XII. 



THEORY OF LOCOMOTIVE ENGINES. 



ARTICLE I. 

OP THB EFFECTS OF THE ENGINES WITH AN INDEFI- 
NITE LOAD OR VELOCITY. 

Sect. I. Of the different problems which present 
themselves in the calculation of the effects of loco^ 
motive engines. 

The principal problems which occur with respect 
to locomotive engines have reference in the first 
place to two circumstances, namely: I. When the 
engine is already constructed, and the question 
is to determine the effects that it wiU produce; 
II. When the engine is as yet unbuilt, and the 
question is to determine the proportions it ought 
to have in order to produce desired effects. At 
present we consider only the questions relative to 
the first case, and shall reserve the others for the 
following -chapter. 

When an engine is already constructed, and all 
its dimensions may be directly measured, the fol- 
lowing problems may present themselves: 



318 CHAPTER XII. 

1st. To determine the velocity the engine will 

assume, with a fixed load ; 
2nd. To determine the load it will draw at a 

desired velocity; 
3rd. To determine the usefhl effect it will pro- 
duce, at a desired velocity or with a fixed 
load. 
And this last problem may, itself, he expressed 
under ten different forms, namely, to find suc- 
cessively : 

The useful effect of the engine, in tons drawn 

1 mile; 
The useful effect expressed in horse-power ; 
The quantity of fuel necessary per ton per mile ; 
The quantity of water necessary per ton per mile ; 
The useful effect produced per pound of fuel con- 
sumed ; 
The useful effect produced per cubic foot of water 

vaporized ; 
The consumption of fuel which produces 1 horse- 
power; 
The consumption of water which produces 1 horse- 
power ; 
The horse-power produced per pound of fuel ; 
The horse-power produced per cubic foot of water 

vaporized. 
Moreover, as two cases are necessarily to be dis- 
tinguished in the work of the engines, namely, the 
case in which they work with a load or velocity 
indefinite, and that in which they work with the 



OF THE EFFECTS OF THE ENGINES. 319 

load or velocity which produces the maximum of 
useful effect, there will yet occur in this respect a 
new series of questions, namely : 

1st. To determine the velocity at which the 
engine will produce its maximum of useful 
effect ; 
2nd. To determine the load corresponding to the 

production of the maximum of useful eflFect ; 
3rd. To determine the maximum of useful effect 
that the engine can produce. 
And this last problem may be expressed under the 
ten different forms which we have indicated above. 

We will, then, consider successively these two 
series of questions. 

Sect. II. Of the elements to be considered in the 

calculation of the engines. 

In the attempts hitherto made for calculating the 
effects of steam engines, or for determining the ve- 
locity of the piston under a given load, the cal- 
culation has been grounded on two data only : the 
pressure of the steam in the boiler, and the re- 
sistance of the load against the piston. 

This mode seems to comprehend all the data of 
the problem ; but its erroneousness ought to have 
been recognised, when it was seen that all essays 
made to arrive at any formulae by this means, 
produced nothing that was not annihilated by ex- 
perience. It is more especially in endeavouring to 



320 CIIAPTBR XII. 

apply this method or these formulae to the motion 
of locomotive engines, in order to determine the 
load they can draw at a given velocity, or the 
velocity they can assume under a given load, that 
the calculator is quickly led to results which are 
palpably inadmissible. 

The cause of this appears in these two facts : 1st. 
That the pressure of the steam in the boiler, even 
supposing it to represent exactly the pressure in the 
cylinder, or the effort applied against the piston, 
would be far from offering, on that account, a 
complete measure of the power of the engine, that 
is to say, of the motive force of which it can dispose, 
and could not therefore be sufficient to calculate its 
effects : 2nd. That the pressure in the boiler does 
not represent the pressure in the cylinder, or the 
effort appUed against the piston, but can only fix its 
extreme limits, that is to say, it can only indicate 
the maximum load of which the engine is capable, 
and nothing else. We shall here demonstrate the 
first of these points ; the second will naturally be 
made clear when we come to treat of the pressure 
in the cylinder. 

We say, that supposing the case wherein the 
pressure in the cylinder were equal to the pressure 
in the boiler, that is, the case in which, on mea- 
suring the pressure in the boiler, we should thereby 
obtain the effort applied by the engine, that measure 
would not suffice to make known its disposable 
motive force, nor consequently to calculate the 



OF THE EFFECTS OF THE ENGINES. 321 

effects it can produce. In fact, when we consider 
201 engine in a state of statical equilibrium, or at 
rest, the force which it applies reducing itself to 
a simple pressure, is found completely represented 
by the effort which the engine can exert, or by the 
mass which it can hold in equiUbrium. But when 
we consider engines in a state of motion, the force 
which they apply is no longer a pressure, but a 
motive force ; that is to say, it is no longer Umited 
to the producing of an effort, but an effort and a 
velocity. ITiis force, therefore, is no longer mea- 
sured by the mass which it can hold in statical 
equilibrium, but by the mass which it holds in 
d3mamical equilibrium, that is, in uniform motion, 
and by the velocity which it is capable of com- 
municating to that mass. If then the effect of a 
steam engine were to be calculated in the state of 
equilibrium at rest, it might be sufficient to take 
account, in the calculation, of the pressure of the 
steam, which would make known the intensity of 
the effort applied ; but as, on the contrary, it never 
occurs to compute the effects of these engines, 
except in a <6tate of motion, it follows, that to 
estimate the motive force of which they can dispose, 
or to calculate their effects, we must at once take 
account of the effort applied by the engine, and of 
the velocity with which it can maintain that effort. 
Now, in steam engines, the pressure of the steam 
indicates only the mass which the engine can hold 
in equilibrium, and it is the velocity of the production 

Y 



322 CHAPTER XII. 

of the steam alone which indicates the velocity 
which the engine can communicate to that mass. 
Hence it is only hy introducing these two elements 
into the calculation, that an exact valuation can be 
attained of the effects which will be produced. 

The velocity of production of the steam is nothing 
more than the quantity of steam generated in a 
given time. Thus, the power of an engine resides 
at once in the greater or less quantity of steam 
which it produces, and in the degree of pressure 
or elastic force of that steam. In this valuation, 
the pressure is visibly no more than the means of 
verifying the state of the force, at the moment 
when in a manner its quantity is measured; and 
this explains why, in the statical equilibrium, that 
is, when no velocity is produced, and it therefore 
becomes useless to consider that quantity, the 
pressure suffices to represent the power; but it m 
otherwise in the state of motion, because then, as 
we have seen above, the pressure of the steam is but 
one of the elements to be considered. 

We may besides obtain conviction, by more prac- 
tical considerations, that the pressure of the steam 
in the boiler cannot suffice to determine the velocity 
of the engine with a given load. If, in effect, a loco- 
motive engine be put to trial, weak as it may be on 
the score of vaporization, it is easy, by loading the 
safety-valve with 50fts. per square inch, to fill the 
boiler with steam at that effective pressure, or, 
which means the same, at the total pressure of 65fts. 



OF THE EFFECTS OF THE ENGINES. 323 

per square inch. If then a load of 100 tons be 
attached to the engine, let which be the greatest 
load it can draw with an effective pressure of 50]bs. 
per square inch, will it be said that the engine must 
necessarily draw that load at a certam fixed velocity 
which shall depend only on the pressure in the 
boiler and the resistance to the piston ? Certainly 
not ; for if it happen that the engine transform per 
minute 1 cubic foot of water into steam at the 
pressure of the boiler, it may, by that vaporization, 
produce a certain velocity ; but if it vaporize but 
half that quantity, ceteris paribus, it clearly can fill 
the cylinder but half the number of times per 
minute. Thus the pressure in the boiler may 
remain the same ; but the velocity of the engine, 
with the same load, must necessarily be reduced to 
half. It is plain, then, that the pressure in the 
boiler does not suffice to represent completely the 
power of the engine, or to make known its effects. 

But if, by analogy with other boilers already 
tried, and by a comparison of the extent of heating 
surfaces, we previously estimate what quantity of 
steam, at a given pressure, a boiler is able to pro- 
duce per minute ; or if, with still more efiicacy, we 
fill the boiler with water, and producing in the fire- 
box, by any means whatever, a fire as intense as it 
is in the usual work, we ascertain its vaporizing 
power; then alone we shall know the velocity at 
which the engine can continue its motive effort. 



324 CHAPTER XII. 

and be able to estimate the work it can perform 
in a given time. 

The pressure of the steam in the boiler, taken 
alone, can determine but one thing: viz., the limit 
of the load of the engine, from the necessity which 
exists that the resistance against the piston should 
never exceed the pressure in the boiler, since the 
resistance would then be greater than the power, 
and consequently the motion could not be produced. 
But in every inquiry into which the velocity figures, 
recourse must necessarily be had to the vaporizii^ 
power ; and then the separate influence of each of 
these two elements in the result is this : 

The limit of the load possible for the engine is 
given by the degree of pressure in the boiler ; 

And the velocity with that load, or with any 
other, is given by the vaporizing power. 

These effects will become much clearer as we 
shall develope the theory of the engine; but we 
thought it right to explain them here in a summary 
way, to show from what motive we entirely lay 
aside the ordinary mode of calculation applied to 
steam engines. Since the first edition of this work, 
we have published, under the title of Tlieory of the 
Steam Engine, a work in which we have developed 
at length the proofs of the inaccuracy of the pro- 
cesses in use for calculating the effects or the pro- 
portions of steam engines ; to that work then we 
refer for whatever may not appear to be sufiiciently 
explained here. 



OF THE EFFECTS OF THE ENGINES. 325 



Sect. III. Of the pressure of the steam in the 

cylinder. 

The pressure of the steam in the cylinder is the 
first inquiry that must engage our attention in order 
to be able to determine the effects of the engine. 
It is, in fact, always easy to ascertain the quantity 
of steam generated per minute in the boiler. If 
then we knew also the pressure at which that steam 
is expended in the cylinder, we might immediately 
conclude the velocity which the engine must neces- 
sarily assume; for it would sufiice to divide the 
volume of steam produced, by the contents of the 
cylinder, to have the number of cylinders-fiill of 
steam, and consequently the number of strokes of 
the piston the engine will furnish per minute, which 
will give its velocity. 

At a first glance, it is natural enough to think 
that the pressure of the steam in the cylinder must 
be the same as in the boiler, or at least that it must 
differ from it only according to the losses to which 
the engine may be liable ; but it is easy to obtain 
conviction that such is not the case, and that in an 
engine subject to no loss of any kind whatever, the 
pressure in the cylinder, during the permanent 
motion, may at times be sensibly equal to that of 
the boiler, and at times much less ; which depends, 
not on losses supported by the steam, but on the 
load drawn by the engine. 



326 CHAPTER XII. 

We know, in fact, that in every sort of engines 
the velocity, exceedingly small at first, increases by 
degrees up to a certain point, beyond which it does 
not go, because the mover is not capable of greater 
velocity with the mass which it has to move. If 
the engine is well constructed, and especially if it is 
regulated by a fly-wheel, that velocity, once at- 
tained, maintains itself without alteration, though 
the action of th^ mover may continue to vary, or, 
in other words, to oscillate between certain limits, 
and the motion becomes quite uniform. 

As soon as the motion has attained uniformitv, 
which always happens at the end of a short time, 
and which is the normal state of the engine during 
its work, the mover, which at the commencement of 
the motion 'must necessarily have exerted a force 
greater than the resistance, now expends but the 
force precisely capable of holding that resistance in 
equilibrium ; for were it to apply a force greater or 
less, the motion would be accelerated or retarded, 
whereas by the fact it is uniform. 

Now, in the engines under consideration, the 
force applied by the mover is nothing more than the 
pressure of the steam against the piston, or in the 
cylinder; as soon, therefore, as the engines have 
attained uniform or permanent motion, the pressure 
of the steam in the cylinder is strictly equal to the 
resistance of the load against the piston. 

To account for the manner in which the equi- 
librium of pressure establishes itself in a locomotive 



OF THE EFFECTS OF THE ENGINES. 327 

engine, it suffices to trace its effects from the origin 
of the motion. At that moment, the steam being 
enclosed in the boiler at a certain pressm^, passes 
into the steam-pipes, and thence into the cylinders. 
Entering these, whose area is about 10 times that 
of the pipes, the steam at first dilates, losing propor- 
tionally its elastic force ; but as the piston is not 
yet in motion, and as by reason of the load which it 
supports, it can acquire its velocity but very slowly, 
whereas the steam continues to arrive with rapidity, 
the equilibrium of pressure quickly establishes itself 
between the boiler and the cylinder; and the piston, 
driven by all the force of the steam, begins slowly 
to move in the cylinder. The motion thus im- 
pressed on the piston communicates itself therefore 
to the engine and to all its train, and the entire mass 
acquires a certain velocity. At this moment, if 
the arrival of the steam were suddenly intercepted, 
the piston would not stop on that account; it 
would, itself, be carried on for some time by the 
force which it has previously communicated to 
the moving mass. The result therefore is, that 
at the following stroke, the steam finds the piston 
already moving with a certain velocity, at the mo- 
ment when it comes to impress a new quantity of 
motion thereon; and this new supply of motion 
passes on to the mass, where it continues to accu- 
mulate. Thus, receiving at every stroke a fresh 
impulse, and preserving the former one, the piston 
by degrees accelerates its motion, and the train at 



328 CHAPTER XII. 

last acquires all the velocity the engine is capable of 
communicating to it. 

From what has just been said, we see that at the 
moment of starting, the slowness of the motion 
allows the steam to acquire in the cylinder the 
same pressure as in the boiler, and that it is the 
superiority of that pressure over the resistance of 
the piston which makes the latter more and more 
accelerate its motion, till at last it attains all the 
velocity which it is capable of acquiring with the 
resistance with which it is loaded. But as the 
piston assumes a greater velocity, it in a manner 
flies before the steam, without allowing it time to 
acquire in the cylinder all the pressure it might 
assume there. The action of the steam to ac- 
celerate the motion of the piston, becomes then 
less and less; and finally, when the piston has 
attained the greatest velocity the engine can com- 
municate to it, the accelerating action of the steam 
upon it has become null, since it can augment its 
motion no more. Now, the accelerating action of 
the steam consists in the excess of its pressure above 
that of the resistance. Hence at this moment the 
pressure of the steam in the cylinder and that of the 
resistance against the piston, are precisely in equi- 
librium with each other ; and if the motion of the 
engine remains in a state of uniformity, it is because 
the resistance which is exerted continually, and 
would have for eflfect to retard the motion, is im- 
mediately destroyed by an equal pressure from the 



OF THE EFFECTS OF THE ENGINES. 329 

mover ; whence results that the motion must con- 
tinue the same without alteration. 

In steam engines in general, the uniformity of 
motion is produced by a fly-wheel ; but in locomo- 
tive cingines, it is the mass of the train itself which 
performs the office of a fly-wheel. This mass 
receives and in a manner stores the quantities of 
motion impressed by the mover in its moments of 
greatest action, to restore them afterwards, when the 
mover is in a moment of less force ; and it is from 
the very difficulty of increasing or diminishing the 
velocity of the mass, that the uniformity of motion 
of the whole results. With respect to certain parts 
of the engine, which, like the piston, for instance, 
must necessarily vary in velocity during the time 
of their oscillations, the uniformity of motion in 
question is imderstood to mean an exact conformity 
of time, such that at any point of one oscillation, the 
velocity is precisely the same as it was at the same 
point of the preceding oscillation ; so that if the 
duration of one of these oscillations were taken for 
the unit of time, the motion would be strictly 
uniform. 

We see then, from what precedes, that at the 
commencement of the motion or at the starting of 
the engine, the steam begins by acquiring in the 
cylinder a pressure equal to that of the boiler ; but 
that this state is but transitory, and that as the 
velocity of the piston increases, the pressure in the 
cylinder gradually lowers, till at last it becomes 
precisely equal to the resistance of the load. This 



330 CHAPTER XII. 

equilibrium once established, the velocity of the 
piston ceases to increase, the motion becomes uni* 
form, and the steam continues to expend itself in 
the cylinder at the pressure indicated by the re- 
sistance. 

Thus, we know the pressure at which the steam 
expends itself in the cylinder ; and knowing also the 
volume of the cylinder, we may conclude the abso- 
lute expenditure of steam which takes place at 
every stroke of the piston ; wherefore, comparing 
this expenditure with the total mass of steam of 
which the engine can dispose, we may without 
difficulty deduce the velocity of the motion. 

Sect. IV. Of the velocity of the engine with a given 

load. 

We have just said that with the elements which 
we have at our disposal, we can determine the 
velocity which an engine will assume in drawing a 
given load. 

Suppose, in effect, that a load of 50 tons gross, 
tender included, be drawn up a plane inclined y^, 
by an engine with 2 cylinders 1 1 inches in diameter, 
stroke of the piston 1 6 inches, wheels 5 feet, friction 
103 fts., total pressure of the steam in the boiler 
65 lbs., or effective pressure 50 lbs. per square inch, 
and, finally, vaporizing power nearly such as we 
have found it for the average of the Liverpool and 
Manchester locomotive engines, that is, 60 cubic 
feet of water per hour, or 1 cubic foot per minute. 



OF THE EFFECTS OF THE ENGINES. 331 

We have already found above, Chapter IX., that 
the total resistance opposed by that load to the 
motion of the piston, in the case of this engine, is 
48 lbs. per square inch, when the velocity is 20 
miles per hour. If then we admit that the engine 
will came near enough to that velocity, for the 
valuation which we have made of the resistance of 
the air and the pressure caused by the blast-pipe, in 
the calculation, not to be very far from the truth, 
we must conclude that, during the uniform or 
permanent motion of the engine with that load, 
the pressure of the steam, during its action in 
the cylinder, will Ukewise be 48 lbs. per square 
inch. 

Now the quantity of water consumed by the 
boiler amounts to 60 cubic feet of water per hour, 
and we have shown in treating of the vaporization, 
that out of that mass of water 75-hundredths only, 
on an average, are really converted into steam, and 
that the rest is merely carried away with the steam 
into the cylinders, but in a liquid state. The 
effective vaporization of the engine is then firstly 

•75 X 60 = 45 cubic feet per hour, or 
•75 cubic foot per minute. 

This water is first transformed, in the boiler, into 
steam at the total pressure of 65ft8. per square 
inch ; but on passing into the cylinders it acquires 
the pressure of 48 lbs. per square inch, and we 
know that, in this change, the steam remains al- 



332 CHAPTER XII. 

ways at the maximum density for its temperature. 
Its volume may then be determined by the Tables 
which we have giv^i in Chapter 11., on the volume 
of the steam formed under different pressures. Ac- 
cording to these Tables, the volume of the steam 
formed under the total pressure of 48flto. per 
square inch, is 573 times that of the water which 
produced it. Hence the quantity of water efiec- 
tively vaporized per minute in the boiler, will form 
during its passage through the cylinders, a volume 
of steam expressed by 

573 X -75 = 430 cubic feet. 

On the other hand, the area of each cylinder is 
95 square inches, or in square feet that area is 
represented by '66 square foot; and the stroke of 
the piston is 1 6 inches or 1 '33 foot. Whence the 
capacity of each cylinder, traversed by the piston, is 

•88 cubic foot. 

But, besides the portion traversed by the piston, 
there still exists, at each end of each cylinder, a 
vacant space called the clearance of the cylinder ^ 
which is necessarily filled with steam at each 
stroke. Tlie capacity of this vacant space, re- 
presented by an equivalent portion of the cylinder, 
and steam -ways included, is usually ^ of the part 
of the cylinder traversed by the piston. The real 
capacity, therefore, which is filled with steam at 
each stroke of the piston, is 



OF THE EFFECTS OF THE ENGINES. 333 

•88 X f^ = -924 cubic foot. 

Consequently the number of strokes of the piston 
which the engine will give per minute, by reason of 
its effective vaporization, will necessarily be 

430 



•924 



= 465. 



Now each time the wheel makes one revolution, 
the engine gives two strokes of the piston in each of 
its two cylinders ; and the diameter of the wheel is 
5 feet, which makes 15*71 feet in circumference. 
Therefore at every 4 strokes of the piston, the 
engine advances 15' 71 feet; that is to say, its 
velocity, in feet per minute, will be 

465 

-|-X 15-71 = 1822 feet. 

Fmally, as 1 mile contains 5280 feet, and 1 hour 
contains 60 minutes, the definitive velocity of the 
engine, in miles per hour, will be 

60 
■^^ X 1822 = 20-71 miles. 

Thus we see that the above vaporization will ne- 
cessarily produce a velocity of 20*7 miles per hour 
for the engine ; that is to say, a locomotive engine 
with the given proportions may, if in good order 
and with a well-stocked fire, draw a load of 50 tons 
gross, tender included, up a plane incUned 7^, at 
the velocity of 20*7 miles per hour. 

We shall, in the sequel, refer again to the pre- 



334 CHAPTER xir. 

vious valuation of the velocity of the engine, neces- 
sary to have the resistance of the air against the 
train, and to the variation of the vaporization. We 
only wished, at this moment, to show the mode of 
proceeding of the calculation. 

With regard to the velocity which we have just 
obtained, we must add, that if the engine suffers, 
besides, a loss of steam by the safety-valve, which, 
as we have seen, takes place in a great number of lo- 
comotive engines, there will then be a corresponding 
loss on the efiective vaporizaticm ; and consequently 
the definitive velocity of the engine will be reduced 
in a corresponding proportion. For instance, if the 
engine, like those of the Liverpool and Manchester 
Railway, be liable to a loss of *05 of its vaporization 
in full activity, its definitive velocity, in the case 
above mentioned, will become 

•95 X 2071 = 19-67 miles per hour. 

The calculation will be performed in the same 
manner for every other load and for every other 
engine. Thus, in general, resuming the notations 
precedently employed, in the inquiry upon the re- 
sistance on the piston, that is : 
M, Representing the number of tons of the load, 

tend^ included; 
m. The weight of the engine, in tons ; 
g. The gravity, in pounds, of one ton on the plane 
the engine has to traverse ; this gravity being 
null for the case of a horizontal plane ; 



OF THE EFFECTS OF THE ENGINES. 335 

k. The friction of the waggons per ton, expressed 
in pounds; 

xu The velocity of the engine, in miles per hour ; 

uv^^ The resistance of the air against the train, 
at the velocity t;, resistance expressed in 
pounds; 

p'v, The pressure against the piston, arising from 
the action of the blast-pipe, expressed in 
pounds per square foot ; 

F, The friction of the engine, in pounds ; 

S, Its additional friction, measured as a fraction of 
the resistance, according to what was ex- 
plained in Chapter VII. ; 

D, The diameter of the propelling wheels of the 
engine, in feet; 

d. The diameter of the cylinder, in feet ; 

/, The length of the stroke of the piston, in feet ; 

c, The clearance of the cylinder, represented by 
an equivalent portion of the stroke of the 
piston, and consequently in feet ; 

P, The total or absolute pressure of the steam in 
the boiler, in pounds per square foot ; 

jp. The atmospheric pressure, expressed in pounds 
per square foot ; 

Finally, S the effective vaporization of the engine, 
in cubic feet of water per hour, at the ve- 
locity known or unknown of the motion ; 

D DF 

R=(l+S)[(fc±5r)M±sfm+ui;'] ^+^57 +P+p'v 



336 CHAPTER XII. 

will be the pressure of the steam per unit of surface 
in the cylinder, as has been demonstrated above, 
Chapter EX. 

On the other hand, if we express by /^ the rela- 
tive volume of the steam generated under the pres- 
sure R, a relative volume which will be found in 
the Tables given Chapter 11. ; since S is the volume 
of water vaporized per hour in the engine, it follows 
that 

will be the corresponding volume of the steam under 
the pressure R, that is to say, during its action in the 
cylinders. 

But, expressing by ir the ratio of the circum- 
ference to the diameter, the capacity of each cy- 
linder which is traversed by the piston, has for its 
measure 

and the clearance of the cylinder offers, besides, a 
capacity of 

irrd^c. 

Therefore the totality of the space filled with steam 
at each stroke, in each cylinder, has for its ex- 
pression 

Consequently the number of strokes of the piston 
corresponding to the volume of steam expended /i S, 
will be 



OF THE EFFECTS OF THE ENGINES. 337 



/*= 



But, while each piston performs 2 strokes, that 
is, at every expenditure of 4 cyUnders-full of steam, 
the engine advances 1 turn of the wheel, that is to 
say, a space represented by 

irD. 

Therefore the velocity of the engine, in feet per 
hour, will be expressed by the above number of 
strokes, divided by 4 and multiplied by tt D ; that is 
to say, the velocity will be 

V — ^ ^ 
"■ d«" l+c' 

And finally, as 1 mile contains 5280 feet, the velocity 
of the engine, expressed in miles per hour, will be 

v = J—. -^. -5- (1) 

5280 d"" l+c 

This expression will make known the velocity re- 
quired, on substituting, for each of the letters, the 
value suitable to it in the engine considered. 

As it has been shown. Chapter II., that the rela- 
tive volume of the steam under the pressure R, may 

be expressed by 

1 

n + 5 R 
it is plain that, instead of seeking the relative volume 
fi in the Tables which we have given, its value may 
be represented by the expression 

1 ^ __J . 



338 CHAPTER XII. 

and consequently the preceding expression of the 
velocity of the engine may equally be written under 
the form 

L. i J s (1 1,^3) 

Such then will be the general expression of the 
velocity of the engine, in miles per hour; an ex- 
pression in which all is known from measures taken 
on the engine, even the vaporization S, which re- 
sults from the extent of heating surface, according 
to what has been shown, Chapter X. 

Making use of this formula to find the velocities 
corresponding to divers loads of the engine, or to 
divers values of M, attention must be paid never to 
suppose, for M, a load capable of producing on the 
piston a resistance greater than the pressure of the 
steam in the boiler, because it is evident that the 
resistance would then exceed the power, and the 
motion could not take place. This maximum load 
of the engine will form a special inquiry in Article 
II. of this chapter. Nor can M be supposed of a 
value less than the weight of the tender, which is 
the minimum load an engine can have to draw. 
Beyond these two limits the solutions given by the 
formula would evidently cease to suit the problem. 

As to the velocity resulting from this formula, we 
shall equally see, in the following article of this 
chapter, that, for a given value of the vaporization 
S, it can never be less than a certain quantity which 
we shall determine, and which will consequently 



OF THE EFFECTS OF THE ENGINES. 339 

make known the minimum velocity of the engine. 
With respect to the maximum velocity that the 
engine can attain, it clearly will depend principally 
on two things; the weight of the load, and the 
inclination of the plane on which that load is 
drawn. If we first suppose either an ascending 
inclined plane, or a horizontal plane, or an inclined 
plane descending, but on which the gravity does 
not exceed the friction of the train, it wiU be found 
that the less the load is, the greater velocity the 
engine will assume. If we suppose, on the con- 
trary, a descending inclined plane, on which the 
gravity exceeds the friction of the train, it will be 
found that the more the plane is inclined, and the 
heavier the train is, the more the velocity of the 
motion will increase, because the excess of the 
gravity above the friction will be by so much 
more considerable, and that this force acts in 
favour of the motion. But it is not to be supposed 
that on a plane exceedingly inclined, or with a very 
heavy load, the velocity of the motion can ever 
increase indefinitely. The slightest essay of cal- 
culation on the preceding formula will immediately 
demonstrate this ; and the reason of it will readily 
be conceived, on observing that by degrees as the 
gravity and the efibrt of the engine tend to augment 
the velocity of the train, the air opposes, on the 
contrary, more resistance, and a resistance more- 
over which increases in the ratio of the square of 
the velocity. We shall see, therefore, Chapter 



340 CHAPTER XII. 

XVII., that the engines^ when descending inGlined 
planes, assume much more moderate velocities than 
one would be tempted to admit at a first view. 

It is to be remarked that the formula which we 
have just obtained for the velocity of the engine, 
still contains, in the second member, the two terms 
uv^ and p'v^ which are functions of v, and whose 
value cannot consequently be precisely found with- 
out knowing the velocity v itself, which is the 
quantity sought. Were it desired to disengage the 
unknown quantity entirely, those two terms must 
be eliminated from the second member of the equa- 
tion ; but to avoid the equation of the third degree 
which would then result, the formula may be used 
such as it is. In order to eflfect this, a probable 
estimation must first be made of the quantity r, and 
by means of it an approximation of the two terms 
uv^ and p'v will be furnished ; then substituting 
these in the formula, a certain value of v will be 
deduced. If this value coincide with that which 
has been supposed to determine the two terms 
uv^ and p v, or at least differ from it only in an 
inconsiderable degree, it will be the true value of 
V, since it will completely satisfy the equation. If, 
on the contrary, the value of v thus found differ too 
much from that which has been supposed in the 
determination of uv^ and p'v, for these two terms to 
be considered as having been properly estimated, 
the value of v obtained by this first calculation must 
be employed, to estimate with more precision the 



OF THE EFFECTS OF THE ENGINES. 341 

two terms uv^ and p'v ; then, substituting them in 
the equation, a second value of v will be attained, 
more approximate than the first. This second 
value, should it not appear sufficiently exact, would 
serve in the same manner to find a third ; but with 
a little practice in the calculation, two trials will 
always be found sufficient, and the recurrence of 
the same numbers will so simplify the research, 
that a third trial, in case of need, will be made 
without the least difficulty. 

K it be wished to take account in the calculation 
of the variations which the vaporization of the 
engine undergoes by reason of the velocity, ac- 
cording to what has been shown. Chapter X., the 
given vaporization will be that which is known for a 
certain determined velocity, that is, it will be, for 
that velocity, the value of the quantity S then 
supposed variable. In this case, the same process 
must be used in determining S, as has just been 
explained for the quantities p'v and uv^. Thus, 
having made a previous estimation of the velocity, 
the corresponding values of S, p'v and uv^ must be 
deduced, and the equation solved with them. If the 
resulting value of v do not coincide with the sup- 
position made, the latter must be corrected, as has 
been said above. This shall be illustrated further 
on by an example. 

We have yet to observe that the value of i;, in the 
equation (1 bis), or the expression of the velocity of 
the engine, is entirely independent of the pressure in 



342 CHAPTER XII. 

the boiler. This result has nothing suqprising ; for 
we have proved that the steam assumes^ in the 
cylinder, a pressure strictly indicated by the restst- 
ance of the piston, and that moreover, in this 
change, the steam remains at the maYimum density 
for its temperature, as if it rose immediately from 
the liquid at that very pressure. Hie consequence 
is therefore, that it matters little whether the steam 
has been originally produced in the boiler at any other 
greater pressure, since that pressure in the boiler is 
but a transitory state which ceases to subsist, and of 
which no trace remains, as soon as the steam begins 
its action. If, for instance, the resistance of the pis* 
ton, and consequently the total pressure of the steam 
in the cylinder, is 50 lbs. per square inch, is it not 
true, that provided the steam be abundantly fur- 
nished at that pressure by the heating surfece, it is 
quite indifferent whether till the moment of being 
used, it has been stored in the boiler under a 
pressure of 65, or 75, or 95 lbs. per square inch ? 
That steam must always, definitively, at the moment 
of action, be transformed into steam at only 50 flbs. 
of pressure ; and the velocity will depend solely on 
the quantity of steam at the pressure of 50 lbs., 
which shall have been furnished by the boiler. It 
is very erroneously then that engine-men are fre- 
quently seen to augment the pressure in the boiler 
of the engines, in the hope of obtaining a greater 
velocity. It is the vaporization, and not the pres- 
sure, that must be augmented, and it is very 



OF THE BFFBCTS OF THE ENGINES. 343 

probable that if the truth, in this respect, were more 
generally known, steam engines, and particularly 
those of steam vessels, would be liable to fewer 
explosions ; for a great number of those accidents 
are to be attributed to the desire of obtaining a 
greater velocity, which the engine-man flatters him- 
self of being aUe to attain by augmenting consider- 
ably the pressure in the boiler, by means of the 
safety-valves. 

With regard to the quantities contained in the 
formulae, we have indicated above the manner in 
which each of them ought to be expressed, and it 
will have been remarked that we have referred all 
the measures to uniform unities, namely : the foot, 
the pound, and the hour, as respective unities of 
length, weight, and time. The observation of this 
rule is absolutely indispensable, in order that the 
formulae may be what is called homogeneous^ and con- 
sequently that they give an exact result. This is 
a remark on which we deem it necessary to insist, 
because, in practice, some of the quantities which 
we employ are expressed in inches, others in pounds 
per square inch, or sometimes in atmospheres, &c., 
according as it may seem most commodious for 
common use ; and if all these measures were not 
restored to homogeneity, none but a most erroneous 
result could be obtained. 

In order however that no difficulty may occur on 
this head, we shall, in the sequel, resume this 
subject, in transforming the obtained formulae into 



344 CHAPTER XII. 

practical formulae, and shall then give an example 
of the application of each of them. 

Lastly^ before passing to another, problem, we 
most yet remark that the formula which we have 
obtained above, differs in appearance from that 
which we have given for the same purpose, in the 
work entitled Tlieory of the Steam Engine. But the 
reason is merely that some of the terms in it are 
more developed, and, besides, that the velocity 
here calculated is that of the engine and not of the 
piston, which has obl^ed us to refer the different 
resistances, not to the velocity of the piston, as in 
the work just cited, but to the vekxuty of the engine 
expressed in miles per hour. 



Sect. V. Of the load of the engine for a desired 

velocity. 

The object of the preceding research was to 
determine the velocity of the engine for a fixed 
load. But if, on the contrary, the velocity be given, 
and that it be desired to know what load the engine 
can draw at that velocity, on a plane of a deter- 
mined inclination, then it will suffice to resolve the 
equation (1 bis) with reference to M, and we shall 
have for the value of M, 

This equation then will make known the load, in 



OF THE EFFECTS OF THE ENGINES. 345 

tons gross, tender included, which corresponds to 
the velocity v. 

It is necessary, however, here to observe that there 
are many ways of expressing the load of the engines 
in practice. It is most commonly expressed as we 
have done it, in tons gross, tender included, that is, 
including the weight of the tender of the engine. 
But, for certam inquiries, it is more convenient to 
express it, either in tons gross, tender not included ; 
or in elective tons of goods, that is, exclusive both 
of the tender and of the waggons. To pass from 
the first of these expressions to the two others, we 
have evidently but to subtract the weight of the 
tender in the first case, and the weight of both 
tender and waggons in the second. 

Thus, expressing by C the weight of the tender, 
the load of the engine, tender not included, will be 

M-C; 

and expressing by - the average ratio of the weight 

of the goods carried on a waggon, to the total 
weight of the loaded waggon, 

i(M-C) 
t 

will be the load of the engine in effective tons. 

On railways of not more than about 5 feet of 
breadth of way, and for an engine weighing from 8 
to 12 tons, the average weight of the tender may be 
valued at 6 tons, and the efiective load of the wag- 



346 CHAPTER XII. 

gons is commonly f of their total weight. We have 
then for the different expressions of the load, 

M, load in tons gross, tender included ; 

M— 6, lottd in tons gross, tender not incladed ; 

•|M->4, load in effective tons. 

It must be observed that the formula which we 
have just obtained, contains in its second member 
the term wt;*, in which u depends on the number of 
carriages in the train, as has been seen, Chapter IV. 
The precise value of this term could not then be 
determined till after the load of the engine be 
known, which is the quaesitum of the problem ; but 
recourse will be had to approximations, as in the 
preceding research : that is to say, the second mem- 
ber of the formula must be calculated, exclusively of 
the term in which the quantity u figures, and calling 
B the result of that calculation, we have 

Ic±g 

Then making a first valuation of the quantity w, and 
substituting it in the equation, we shall conclude a 
corresponding value of the load M. If that load be 
such as to require for u the value supposed, or very 
nearly so, it is the load sought, and the problem 
is solved. But if the load thus found show that the 
value supposed for u was erroneous, it must be used 
to make a new valuation of u more exact than the 
first: this will consequently lead to a new deter- 
mination of M, which will likewise be more approx- 



OF THE EFFECTS OF THE ENGINES. 347 

imate than the fonner; and were it necessary, a 
third approximation might be made. But in general 
two trials will suffice ; be it as it may, the equation 
is so simple, that these essays will be made rapidly 
and without the least difficulty. 

Examining the formula which we have obtained 
above for the load of the engine, it will be remiarked 
that taking the cases wherein g is preceded by the 
sign minuSy and making k—g^=^Oy that is, supposing 
the motion to take place in descending an inclined 
plane on which the friction of the waggons is 
counterbalanced by their gravity, the formida seems 
to give, for the suitable solution of the problem, 

M=i. 



But this apparent result depends only on the cir- 
cumstance that un^ is not developed, and that it is 
really a function of M. In effect, we have seen, 
Chapter IV., that the value of wv', which represents 
the resistance of the air, depends not only on the 
transverse section of the train, but likewise on the 
number of carriages which compose it, and conse- 
quently on the weight of the train. The result 
obtained above is then caused simply by the co- 
efficient of the only term in which the quantity M 
is expressed, becoming null by the supposition of 
ft — 9=0 ; but it will presently appear that referring 
to the value of the term wi;*, the weight, of the load 
M is no less limited and easy to determine. 



348 CHAPTER XII. 

In effect, if we resume the equation (2) and write 
it under the form 

(*±ir)M±^ + «r3=-i-rJ^. ' ?.- F- ^ll+p + p'v)], 

l + aL5280 /+e 90 D\q ^ fj 

it will be recognised that the first member expresses 
the total resistance opposed by the train, namely, 
the gravity and friction of the waggons, the gravity 
of the engine, and finally, the resistance of the air 
against the train. But if, in this equation, we make 
k—g=^Oy it becomes 

that is to say, in this case, the resistance of the train 
reduces itself to that of the air diminished by the 
gravity of the engine. The quantity M then osten- 
sibly disappears firom the equation, but it neverthe- 
less remains represented by the term uv^y and by 
this term will be obtained the solution sought ; for 
resolving the equation with reference to wt;^, we 
derive 

--n:.tii,-,4-4-'-*'(r*'*'--)]*'- 

Now the velocity of the motion is given. There- 
fore this equation will make known the quantity u , 
and, as a consequence, the effective surface offered to 
the shock of the air by the train in motion. But 
we have seen. Chapter IV., that, for a railway of 5 
feet of width of way, that efiective surface is equal 
to 70 square feet, plus as many times 10 feet as 
there are waggons. We may then, from the know- 



OF THB EFFECTS OF THE ENGINES. 349 

ledge of II, deduce the number of carriages/ and as 
we know besides the average weight of a carriage, 
we shall conclude, in fine, the definitive weight of 
the train, which will be limited and not infinite. 

There is yet another case in which the formula 
just obtained for the load of the engine, seems to 

give the result of M= - : it is the case wherein 



it is supposed t; = o. The consequence then would 
be that the load corresponding to a velocity null 
would be infinite. But observing the formula more 
attentively, we recognise that it by no means gives 
this result. It will be recollected, in effect, that 
the quantity S represents the effective vaporization 
of the engine, or the volume of water which really 
passes, in the state of steam, into the cylinders. 
Now if we suppose the velocity null, it is evident 
that no steam at all can pass into the cylinders, 
since that steam could not traverse them without 
driving the pistons, and consequently creating some 
velocity in the engine. The supposition therefore 
of r = necessarily carries with it that of S = o, 
and consequently the value of M then presents itself 
under the form 



Thus, in this case, the formula reduces itself to the 
indeterminate form; but it must be observed that 
the formulae under consideration are intended to 



350 CHAPTER XII. 

make known the effects of the engine, only when 
it has attained unifonn and permanent motion. 
Now it will presently be seen, in seeking the velo- 
city of maximum useful effect, that for a given 
vaporization S, the uniform velocity of the engine 
can never be less than 

._ 1 S JD^ 1 

^ ~5280' d«' l+c n+jP' 

because this velocity is that which corresponds to the 
passage of the steam into the cylinders in its state of 
greatest density or highest pressure, and that at any 
other less density, the steam would necessarily oc- 
cupy a greater volume, and consequently could not 
traverse the cylinders without producing a greater 
velocity in the engine. All supposition of a smaller 
velocity than the above is therefore inadmissible in 
the problem, as being incompatible with the state of 
permanence and uniformity of motion for which 
alone the effects of the engines are calculated. 



Sect. VI. Of the different expressions of the useful 

effect of the engine. 

We have said that there are many modes of 
expressing the useful effect of the engines. We 
are about to consider each of them successively. 

1st. The useful effect produced by an engine in a 
given time, is the product of the mass conveyed 
and the distance to which it is conveyed, in the 



OF THE EFFECTS OF THE ENGINES. 351 

given time. Now, in the engines under considera- 
tion, the mass conveyed is represented by the 
quantity M, or by the number of tons drawn by 
the engine. The velocity t; likewise expresses the 
distance traversed by the engine, or, in other words, 
the distance traversed by the load, during the unit 
of time. Hence the product M i; is no other than 
the useful effect produced by the engine during the 
unit of time. 

To obtain the expression of this useful effect, it 
wiU consequently suffice, to draw from equation (2) 
the value of M t;, which will be done by multiplying 
both terms by v ; and thus we shall have 

(l + 8)(*+^) L5280 i+e q V \q / J *±^ 

We have thus the solution of the problem ; and it 
will be observed that this expression of the useful 
effect, for a given vaporization S, varies with the 
velocity of the engine, as may have been already 
remarked in the experiments which we have pre- 
sented, Sect. II. Chapter XL 

In practice, the desired result may be attained 
more simply, by seeking first, from equation (2), 
the numerical value of the load M corresponding 
to the velocity t;, then multiplying that load by the 
given velocity. For instance, we have already 
found. Sect. iv. Article I. of this chapter, that at 
the velocity of 19'67 miles per hour, and ascending 
a plane inclined j^, an engine of the dimensions 



352 CHAFTEE Xll. 



before indicated, would draw a kiad erf* 50 tons. 
We are then to condnde that the nsefbl dEkdt 
which the esu^ne will prodace at that velocity and 
on that plane, will be 983 tons omveyed 1 mile per 
hour. 

Hie solution whidi we have just given oi the 
problem suits the case in which it is required to 
find the useful effect produced at a kno¥m velocity. 
But if, on the contrary, the load is given, and it be 
required to find the useful effect that the engine 
will produce with that load, then the velocity 
corresponding to the ^ven load must first be 
sought, finom equation (1) or (1 bis), and that 
velocity multiplied by the given load will be the 
corresponding useful effect. 

We must here call to mind that the load M of 
the engine is measured in tons gross, tender in- 
cluded, and consequently the useful effect Mv is 
the useful effect of the engine in tons gross dra?m 
1 mile, tender included. But as we have seen that 
representing by C the weight of the tender, and by 

-r the ratio of the effective load of a waggon to its 

total weight, the load of the engine may be ex- 
pressed m tiuee ways, namely: 

M, . . • . load in toDB gross, tender incloded ; 
M— C» . . load in tons groas, tender not included ; 

-r (M^C)» load in effective tons ; 
t 

it is plain that the useful effect of the engine, in 



OF THE EFFECTS OF THE ENGINES. 353 

tons drawn 1 mile, may be likewise expressed in 
three ways, which are : 

Mv, .... useful effect, in tons gross drawn I mile, tender 

included ; 
Mv— Cv, . useful effect, in tons gross drawn 1 mile, tender 

not included ; 

-- (M^C) V, useful effect, in effective tons drawn 1 mile. 
t 

We have already said that on railroads of but 
about 5 feet of width of way, the average weight 
of the tender may be valued at 6 tons, and the 
effective load at f of the gross load ; we have there- 

fore C = 6 and ^ =f . Thus in the example above 

mentioned, the useful effect of the engine, in tons 
gross drawn 1 mile per hour, may be expressed in 
the three following manners : 

983 tons gross drawn 1 mile, tender included ; 
865 tons gross drawn 1 mile, tender not included ; 
577 effective tons drawn 1 mile. 

The three modes which we have just indicated to 
express the load, and consequently the useful effect 
of the engines, are all in use ; the choice among 
them depends merely on the object in view at the 
time. As, however, they may easily be concluded 
one from another, and as the most simple consists 
in taking the load, in tons gross, tender included, 
this will be the method which we shall employ. 
The only exception which we shall make to this 

2 a 



354 CHAPTER XII. 

rule, will be in the inquiry as to the expenditure of 
coke and water per ton per mile, in which, to con- 
form to the usual practice, we shall refer the ex- 
penditure to the load, in tons gross, tender not 
included. But, in every other case, we will suppose 
the load and the useful effect measured in tons 
gross, tender included, and it will always be this 
that we intend to signify by the usejul effect of the 
engine, when we do not specify to the contrary. 

2nd. The expression furnished by formula (3), or 
the equivalent mode of calculation which we have 
pointed out, makes known the useful effect of the 
engine, in tons conveyed 1 mile in tm hour. But, 
as we have before said, the useful effect of an engine 
may be expressed under several forms. It will be 
proper then to seek those different expressions. 

A very simple mode of making known the effect 
of an engine, consists in representing it by the 
number of horses that would be required to produce 
the same effect, not at the same velocity, but in the 
same time. With this view, the expression one 
horse-power has been made to designate an efiect 
of 33000 ftsr raised one foot per minute. This 
measure has arisen from the observation having 
been made that a vigorous horse going at a walking 
pace, or about 220 feet per minute, which is the 
most advantageous speed, may, permanently and 
without fatigue, exert an effort of 150fts., or, in 
other words, raise a weight of 150fts. suspended 
at the end of a cord which passes over a pulley. 



OF THE EFFECTS OF THE ENGINES. 355 

It is plain that, in this labour, the useful effect 
produced is 33000 fi>s. raised 1 foot per minute, 
and it is for this reason that this effect is designated 
by the name of horse-pawer; but it would be much 
more exact, as we have remarked in another work, 
to call it horse-effect^ since it is an effect and not a 
force. It would then be said that an engine is of 
so many horse-effect, instead of saying that it is 
of so many horse-power. The expression would 
be more correct; but it suffices to have a clear 
understanding as to the value of the terms. 

To apply the measure which has just been given, 
to the effect of locomotive engines, it suffices to 
observe that the traction of one ton gross, on a rail- 
way, offers a resistance of 6 lbs., that a mile repre- 
sents a length of 5280 feet, and that an hour con- 
tains 60 minutes. Any useful effect then whatever, 
expressed in pounds raised 1 foot per minute, may 
be transformed into tons gross drawn 1 mile per 
hour, by multiplying by the factor, 

60 _ 1 
6 X 5280 ~ 528 ' 

and consequently the force or the effect of one 
horse, expressed in this manner, is represented by 

33000 
^ = 62*5 tons gross drawn 1 mile per hour. 

As soon as the effect of one horse has thus been 
referred to the usual measures on railroads, nothing 



356 CHAPTER XII. 

is more easy than to find the effect of a locomotive 
engine, in horse-power. For that purpose, it evi- 
dently suffices to divide the useful effect Mv already 
obtained, by the new unity adopted. We have 
thus the number of those unities which represent 
the effect M r, and consequently the useful eflfect of 
the engine expressed in horses. Tliis effect then 
will be 

U.E. inHP.= ^. 

625 

It will be remarked that the product M v, or the 
useful effect of the engine, varies with the velocity 
of the motion ; and it will be seen further on that 
this product is by so much greater as the velocity is 
less. 

It is the same with effects produced by horses ; 

for we know that the useful effect due to their 

labour decreases rapidly as their speed increases, 

and that it is only at the most advantageous speed 

that this effect can be valued at 33000 lbs. raised 

1 foot per minute. When therefore the useful 

effect of an engine is expressed, under whatever 

form, it will always be necessary, in order to be 

exact, to relate at the same time the velocity at 

which that effect is produced, or, which amounts 

to the same, the load with which it is produced; 

and if this measure is used in an absolute manner, 

as it is with respect to the horse, it should then be 

understood that the effect indicated is that of the 



OF THE EFFECTS OF THE ENGINES. 357 

most advantageous labour of the engine. As we 
shall presently obtain the measure of the maximum 
useful effect a given locomotive engine can produce, 
we may then also express that useful effect in horse- 
power. It will be this valuation then, that is to 
say, the greatest effect the engine can produce, 
working at the minimum or most advantageous 
velocity, that we shall always intend, when we say 
in an absolute manner that an engine is of the effect 
or of the force of so many horses ; but, in every 
other case, in indicating the effect of an engine in 
horse-power, we shall always express at what velo- 
city or with what load such effect is produced. 

3rd. In the two preceding questions we have ex- 
pressed the total effect the engine can produce in 
the unit of time, without regard to its consumption 
of water and fiiel. We are now going, on the con- 
trary, to express that effect with reference to the 
expense which is necessary to produce it. 

The useful effect obtained in equation (3) , is that 
which is produced by the effective vaporization S of 
the engine, or, in other words, by the total vaporiza- 
tion S' of the boiler ; and as we have seen that this 
vaporization S or S' is that which takes place in the 
unit of time, the corresponding useful effect is also 
the useful effect produced during the unit of time. 
But if it be supposed that to effect this vaporization 
the engine requires the consumption of Nibs, of 
fuel, it is clear that then N lbs. of fuel will be suf- 
ficient to draw 1 mile a number of tons expressed 



358 CHAPTER XII. 

by Mv. Therefore, by a simple proportion, the 
quantity of fuel necessary to draw a ton 1 mile 
will be 

N 



Mi; 



It will, however, be observed that the quantity M 
indicates the load of the engine, tender included. 
The number Mv represents then the number of 
tons, tender included, the conveyance of which 1 
mile has been performed by the weight N of coke ; 
and consequently the • result which we have just 
obtained expresses the weight of coke expended 
per ton gross per mile, tender included, that is, 
taking into the calculation the weight of the tender. 
But if it be desired, as is customary on railways, 
to know the expenditure of fiiel which will be neces- 
sary for a given work, tender not included^ recourse 
must then be had to the expression of the useful 
effect of the engine, in tons 1 mile, tender not 
included. We have seen that expressing by C the 
weight of the tender, the useful effect of the engine 
expressed in tons gross conveyed 1 mile, tender not 
included, is 

(M-C)i; = Mt;-Ct;. 

Since, therefore, this effect is produced by the con- 
sumption of N lbs. of coke, the quantity of coke, in 
pounds, necessary, per ton gross per mile, tender not 
included, will be expressed by 



OF THE EFFECTS OF THE ENGINES. 359 

N 



Q. CO. pr. t. pr. m. = 



Mr-Ct; 



To apply this formula it will suffice to know the 
number of pounds of coke consumed in the fire-box, 
to operate in the boiler the total vaporization S' ; 
which the experiments developed Chapter XI. have 
enabled us to do. It will therefore be easy to solve 
the problem proposed. 

It is yet to be observed that the quantity of coke 
necessary per ton per mile, must vary in the same 
engine, with the velocity of the motion; because 
the product M t; is by so much the smaller as the 
velocity is greater, whereas we have shown, in 
treating of the fuel, that the quantity N, or the 
expenditure of coke necessary to operate a deter- 
mined vaporization, varies but in an insensible de- 
gree with the velocity. This result as to the vari- 
ation of fuel per ton per mile has already been 
noticed, Chapter XI. 

4th. From what we have said above, the effective 
vaporization S has sufficed to draw 1 mile a number 
of tons gross expressed by M v, tender included, or 
by (M— C) Vy tender not included. The quantity 
therefore of water effectively vaporized, which has 
performed the conveyance of a ton 1 mile, tender 
hot included, is expressed by 

S 
Mv — Cv 

But as it is more convenient to refer the useful 



360 CHAPTER XII. 

effect to the total or gross vaporization of the 
boiler, and as we have expressed this by S', we 
shall have for the quantity of total vaporization, 
necessary to draw 1 ton gross 1 mile, tender not 
included, 



Q. wa. pr. t. pr. m. = 



Mv-Cv 



5th. To obtain the useful effect produced per 
pound of fuel, it is to be observed that, since the 
useful effect M v has been produced by the consump- 
tion of N lbs. of coke, the useful effect produced by 
each pound of coke must be the Nth part of the 
above effect. Thus this useful effect, expressed in 
tons gross drawn 1 mile, tender included, will be 

U. E. lib. CO. = -=r=- 

N 

6th. Similarly, to obtain the useful effect pro- 
duced per cubic foot of water vaporized, it will be 
observed that, since the useful effect Mt; is that 
which is due to the total vaporization S' of the 
boiler, that is to say, to the number S^ of cubic feet 
of water vaporized, the useful effect produced by 
the vaporization of 1 cubic foot of water will be 
had by dividing the useful effect M t; by the number 
of unities that there are in S\ 

Thus the useful effect produced per cubic foot of 
total or gross vaporization, and expressed in tons 
gross drawn 1 mile, tender included, will be ex- 
pressed by 



OF THE EFFECTS OF THE ENGINES. 361 

Mv 



u. E. 1 ft. wa. = 



S' 



7th. We have obtained, in the 5th problem, the 
useful effect produced per pound of fuel. It will 
therefore be easy to deduce the number of pounds 
of fuel necessary to produce the effect of one horse. 

* 

A simple proportion will evidently suffice, and the 
quantity of fuel, in pounds, which produces the 
effect of one horse, will be expressed by 

62-5 N 



Q. CO. pr. HP. = 



Mv 



8th. We find in the same manner, by a simple 
proportion, the quantity, in cubic feet, of total 
water vaporized, which produces the effect of one 
horse, namely : 

r\ xjD 62-5 S' 
Q. wa. pr. HP. = — .— 

Mv 

9th. The effect, in horse-power, produced by the 
consumption of 1 ft. of fuel, will evidently be 

Mv 



u. E. in HP. of 1 ft. CO. = 



62-5 N 



And, 10th, finally, the effect, in horse-power, pro- 
duced per cubic foot of total water vaporized, will 
be expressed by 

u. E. in HP. of 1 ft. wa. = ^^^. 

625 S 



362 CHAPTEE XII. 



ARTICLE 11. 

OP THE MAXIKUlf U8BFUI« EFFECT OF THE ENGINE. 

Sect. I. Of the velocity of maximum useful effect. 

We have hitherto detennined the effects of the 
engines in a maimer perfectly general, that is to 
say, taking the data of the prohlem without re- 
stricting them to any condition, except only that 
of being contained within the limits of the power of 
the engine. But an important question now pre- 
sents itself. It is proposed, among all the different 
velocities that can be imagined for the engine, and 
each necessarily implying a certain corresponding 
load, to determine that which will produce the 
greatest useful effect. This problem is of great 
utility, since it shows in what case the engine will 
work in the most advantageous maimer possible. 

To solve this question, we must recur to the 
general expression of the useful effect produced by 
the engine, and seek what value of v will make it a 
maximum. This general expression is given by equa- 
tion (3) , namely : 

Now, in observing this expression, we find that 
the velocity figures only in the negative terms ; for 



OP THE MAXIMUM USEFUL EFFECT. 363 

the factor ; could become negative, that is, change 

the apparent sign of the other terms, only in the 
case wherein the motion should be descending, and 
wherein at the same time we should have g>k. 
But in that case the train would be found placed on 
an inclined plane on which the waggons would roll 
of themselves; and consequently the useful effect 
Mv would no longer be the result of the force 
of the engine alone, but of that force joined to the 
gravity^ which would become an effective motive 
force. To know therefore the conditions which 
render the useful effect of the engine a maximum, 
this case must be excluded ; and thus we see that, 
in the expression brought forward, so long at least 
as it expresses only the effect proper to the engine, 
the velocity figures only in the negative terms. 
Hence, firstly, the greatest useful effect will take 
place at the lowest value of v. 

But, from equation (1), the velocity v is ex- 
pressed by 

1 iiS D 



V = 



5280 d^ l + c' 



and it is clear that, for given dimensions and vapor- 
ization, this expression will be at its lowest value, 
when fi is the smallest possible. On the other 
hand, as the quantity fi represents the volume of 
the steam under the pressure R, it will evidently be 
at its least value when the pressure, or resistance R 



364 CHAFTEE XII. 

against the piston, shall, on the contrary, be at its 
maximum. Hence, finally, the maximnm useful 
effect of the engine takes place when the load is 
the greatest possible. 

Now, it is plain that, the resistance R can in no 
case exceed the pressure of the steam in the boiler, 
since the resistance would then be greater than the 
motive power, and the motion would thus become 
impossible. The maximum therefore of R, the 
minimum of r, and the maximum possible useful 
effect of the engine, will be given by the conditional 
equation 

R=P. 

Consequentiy, if we express by ik the relative 
volume of the steam generated under the pressure 
P of the boiler, the velocity of maximum useful 
effect will be determined by putting ii! instead of 
Ik in equation (1) ; that is to say, that velocity 
will be 

1 /S D ,., 

5280 d« l^c ^ ^ 

or else, by putting for lu its value, 

.^ 1 
^ ~n+}P' 

that velocity may again be expressed by the formula 

- 1 S D 1 , - , . , 

V = ^^^^ - -- • -; • =r- .... (4 bis) 

5280 e? /+c n+^P ^ ^ 

This equation then will make known the velocity 
corresponding to the maximum useful effect of the 



OF THE MAXIMUM USEFUL EFFECT. 365 

engine, as soon as the quantities S, d, D, / and P 
shall be replaoed by their value taken on the engine, 
and referred to homogeneous measures, as has been 
already said. 

Sect. II. Of the load corresponding to the maximum 

of useful effect. 

The load corresponding to the maximum of useful 
effect will be known by equation (2) , on substituting 
in it instead of v, the value v' given above. But it 
will be obtained more simply, by deducing it di- 
rectly from the condition 

R=P, 

which, substituting for R its value (Chapter IX.), 
becomes 

(1 + 8) [(*±^)M tgm + iii;»] -?^ + ^ +/> + A=P, 

and which, when v is replaced by v\ gives 

^'-(TH|b5(^-'-'''^-iF/-ni ±'")-:S ^*> 

This formula, in which account must be taken of 
the variation of the term wv'^, as has been said, 
Sect. V. of the preceding article of the present chap- 
ter, will make known the load that ought to be given 
to an engine to make it produce its maximum useful 
effect. 

It is necessary here to remark, that as this load 
offers a resistance precisely equal to the pressure of 



366 CHAPTER XII. 

the steam in the boiler, and as we have seen that at 
the moment of starting of every engyie, the power 
must necessarily exert an effort greater than the 
resistance, it would be impossible for the engine 
to set itself in motion with the load M'. If then 
we would make the engine work with this load, 
it is understood that the aid of another engine 
would be requisite to start it ; or else the engine- 
man must for a few minutes close the safety-valve, 
to create in the boiler a sufficient excess of pressure, 
till the uniform motion be attained. Then the mo- 
mentary excess of pressure may be withdrawn, and 
the engine will continue its motion without any 
external aid. 

However, as on railways there continually occur 
little inequalities or accidental imperfections in the 
road, and as the engine ought to be capable of over- 
coming them, it is not to be expected that it can 
be made to perform an entire trip, working pre- 
cisely at its maximum of useful effect, or with its 
maximum load. The preceding determination there- 
fore is to be considered only as showing what the 
engine may perform on arriving with a velocity 
already acquired, at an inclined plane situated at 
a certain point of the line, or as indicating the 
point towards which our aim should tend as much 
as possible, in order to accomplish producing the 
maximum of useful effect, but without reckoning on 
obtaining it completely in practice. 

We here neglect the little necessary difference 



OF THE MAXIMUM USEFUL EFFECT. 3C7 

between the pressures in the cylinder and in the 
boiler, from the flowing of the steam from the one 
vessel to the other. It plainly tends somewhat to 
reduce the load of the engine, increasing in a cor- 
responding manner the velocity of maximum useful 
effect. 



Sect. III. Of the measure of the mcurimum useful 

effect of the engine. 

The maximum usefiil effect of the engine will 
evidently be the product M'v\ Consequently, 
after having determined the velocity and the load, 
as has just been explained in the two preceding 
sections, it will suffice to multiply together the two 
quantities obtained. Thus we shall have 

m. u. E. = M'i;' (6) 

The developed expression of the maximum useful 
effect might be obtained immediately, by performing 
the multiplication of the two values of v' and M' 
given by the equation^ (4 bis) and (5) ; but as it 
is much more simple to solve these two equations 
separately to derive v' and M' from them first, and 
then to multiply the two results together, as has 
just been pointed out, we will follow this mode of 
calculation. 

To obtain the effect of the engine in horse-power, 
when working at its maximum of useful effect, and 
in like manner to obtain all the other modes of 



368 CHAPTER XII. 

expressing the effect produced, it evidently will 
suffice to substitute, in the general formulae given 
on this head in the preceding article, for the pro- 
duct Mr, the product M'l?', which is suitable to 
the production of the maximum useful effect. We 
shall not dwell here on the divers expressions, since 
they would be but the reproduction of the formulae 
already explained. 



ARTICLE III. 

PRACTICAL FORMULiE FOR CALCULATING THE EFFECTS 
OF LOCOMOTIVE ENGINES^ AND EXAMPLES OF THEIR 
APPLICATION. 

We have hitherto presented the formulae proper 
for calculating the effects of the engines, under a 
form completely algebraical, that is to say, leaving in 
them all the quantities represented by letters, with- 
out excepting the constant quantities whose values 
have been already determined in former chapters. 
But we now purpose to reduce these formulae to 
their most simple practical form ; in order to effect 
which, it will be proper to replace in them, as far as 
may be, the letters by the numerical values which 
they represent. 

'The letters which have a constant value in all 
cases and for all the engines are : 
ky Friction of the waggons, which we have found 
equal to 6 lbs. per ton ; 



PRACTICAL FORMULiE. 369 

jp, Atmospheric pressure, the. value of which is 

21 18 lbs. per square foot; 
n, Constant quantity relative to the volume of the 

steam, its value being '0001421, when the 

pressure is measured in pounds per square 

foot; 
9, Factor relative to the volume of the steam, equal 

to .00000023 when the pressure is expressed 

in poundfl per square foot ; 
c. Clearance of the cylinder, which may be taken 

generally at ^ of the useful stroke of the pis- 

ton, which gives -— — = — -. 

^ l + c 21 

These values being constant for all engines, may 
be introduced permanently into the equations. Sub- 
stituting them therefore for the respective letters, 
and effecting the calculation as much as possible, 
we obtain the following formulae, which are quite 
prepared for practical applications. 

In order to avoid recurring to another page of 
the work, we will first repeat here the signification 
of all the letters which subsist in these formulae. 

M, Load of the engine, in tons gross, tender in- 
cluded ; 

m. Weight of the engine, in tons ; 

C, Weight of the tender, in tons ; 

gy Gravity, in poimds, of 1 ton placed on the in- 
clined plane to be traversed by the engine. 

2b 



370 CHAPTER XII. 

If the inclinatioii of the plane be -, that gra- 
vity will have for its value, in pounds, ; 

and if the plane be horizontal, the gravity 
will be equal to zero ; 

17, Velocity of the engine, expressed in miles per 
hour; 

vr^. Resistance of the air against the train, at the 
velocity 17, a resistance expressed in pounds ; 

p^v. Pressure owing to the blast-pipe, expressed in 
pounds per square foot ; 

F, Friction of the engine, in pounds ; 

S, Additional friction of the en^e, measured as 
a fraction of the resistance, namely : '14 for 
engines with imcoupled wheels, and *22 for 
those with coupled wheels ; 

D, Ditoieter of the propelling wheels, in feet ; 

dy Diameter of the cylinder, in feet ; 

2, Stroke of the piston, in feet ; 

P, Total or absolute pressure of the steam in the 
boiler, in poimds per square foot ; 

S, Effective vaporization of the engine, in cubic 
feet of water per hour. It varies according 
to the engines, but may, on an average, be 
valued at *75 of the total or gross vaporiza- 
tion, when there is no blowing of steam at 
the valves ; 

S^ Total vaporization of the boiler, at the velocity 



PRACTICAL FORMULiE. 371 

of the motion, in cubic feet of water pei:. 
hour; 
N, Consumption of coke in the fire-box, in pounds 
per hour. 



PRACTICAL FORMULA FOR CALCULATING THE EFFECTS 

OF LOCOMOTIVE ENGINES. 

General case. 

f»»* -rr, • • • • Velocity of the en- 

(1 + Z) [(6±y)M ±^ + iiii»] + P + ^(2736 +y») gine, in miles per 

hour. 

Load of the engine, 

in tons gross, tender 
included. 

0. E s M 9 Useful effect, in 

tons gross drawn 
1 mile per hour, 
tender included. 

u.B.inHP ""Hx U"^ «®«^' "^ 

horse-power. 

Q. CO. pr. t. pr.m... »— - — — - Quantity of coke 

m pounds, per ton 
gross drawn 1 mile, 
tender not included. 

S' 
Q. wa. pr. t. pr. m.. . «— —_ Quantity of water, 

in cubic feet, per 
ton gross drawn 1 
mile, tender not in- 
cluded. 

u.E.llb.co. =.-— Useful effect pro- 

duced per pound of 
coke, in tons gross 
drawn 1 mile, ten- 
der included. 



372 CHAPTER XII. 

iLB.lft.wa. ....=^^ Uiefid eflfect pro- 

duced per cubic foot 

of tottl T^orizft- 
tioDt in toDi groM 
drawn 1 mile, ten- 
der included. 

Q.co.fr. 1 HP.....=5^|-^ Quantity of coke in 

pounds, which pro- 
duces the eflfect of 
1 horse. 

Q.wa.fr.lHP.....-5?^A Quantity of water, 

in cubic feet, which 
produces the effect 
of 1 hone. 

U.B. llb.co.inHP.--g^l^ Useful effect, m 

horse-power, pro- 
duced per pound of 
o^e. 

u.E.lft.wa.inHP.»g|L!L. Useful eflbet, in 

hofse-power, pro- 
duced per cubic 
foot of totai ^vpOT' 
isation. 



Case of maximum tisejvl effect, 
^-^^ D s 

1-421 + -0023P7'S velocity of man- 
mum useful effect, 

in miles per hour. 

Maximum load of 

the engine, in tons 
gross, tender in- 
cluded. 

itLU.E. «M'9' Maximum nsefol 

effect, in tons gross 
drawn 1 mile per 
hour, tended in- 
cluded. 



PRACTICAL formula:. 373 

We do not give the divers modes of expressing 
the maximum of useful effect in horse-power, &c.y 
because those formulae are the same as in the 
general case, on merely replacing M and v by M' 
and v\ 

That there may be no misunderstanding as to the 
manner of expressing the divers quantities contained 
in the formulae, nor on the manner of performing 
the calculation, we will here give an example or 
two with some detail. 

Suppose then a locomotive of 65 cubic feet of 
total vaporization, at the velocity of 20 miles per 
hour; with cylinders 11 inches or *917 foot in 
diameter, stroke of the piston 16 inches or 1*33 
foot, wheels 5 feet in diameter, not coupled, friction 
103 fts., weight 8 tons, blast-pipe 2*33 inches in 
diameter, total or absolute pressure in the boiler 
65 fi>s. per square inch, and consumption of coke 
per hour 598fi>s. Suppose this engine employed 
on a level railway, of about 5 feet of width of way, 
and let it be required to know what velocity it will 
attain with a train of 10 waggons weighing 56 tons, 
tender included, which is the same aa 50 tons with- 
out tender. 

1st. As the motion takes place on a horizontal 
plane, we have ^ = ; and since the wheels of the 
engine are not coupled, we have S = -14 = ^. 
Moreover, from the ratio which we have found 
between the total and the effective vaporization 



374 CHAPTER XII. 

of the engine, the value of the latter, at 20 miles 
per hour, is 

S = '75 X 65 = 48-75 cubic feet of water per hour ; 

and in fine, from the proportions of the engine, 
we have 

^ ="w' X ^ = -2237. 

This done, to find what velocity the engine 
will acquire in drawing the train of 56 tons, we 
will first suppose that it may be, approximatively, 
23 miles per hour, and we shall then have, for the 
pressure in the blast-pipe, 4 Hbs. per square inch, or 
p'v = 576 lbs. per square foot. As the efibctive 
surface presented to the shock of the air, valued 
according to the mode explained Chapter IV., is 
5'=70 + 10X 12=1 90 square feet, the resistance 
of the air at the velocity of 23 miles per hour, will 
be uv^ = 270. 

Thus the value of v, taken without supposing 
that the vaporization changes with the velocity, 
will be 

^ 784x48-75 

^"^ 114 (6x56 + 270) +103+2237 (2736 + 576) "•^^*^^"' 

This first essay of calculation gives then 24*88 
miles per hour, for the velocity of the engine, 
and we conclude from it that the two terms uv^ 
and p'v which we have calculated on the supposi- 



PRACTICAL FORMULA. 375 

tion of t7 = 23, have not been valued in a manner 
sufficiently exact, but that the true velocity is com- 
prised between 24*88 and 23 miles. 

Trial then might be made of t; = 24, and this 
value would be found to satisfy the problem, when 
the variation which the vaporization undergoes with 
the velocity of the motion is neglected. Thus ap- 
proximatively we might hold to this result ; but if 
it be desired to calculate with greater accuracy, it 
will be proper to introduce the increase of vaporiza- 
tion due to the velocity. 

For this purpose, as the increase of vaporization 
will have the effect of increasing the result of the 
calculation, we will try a number greater than 24, 
as v = 25, for instance. Supposing then this datum 
for the valuation of the variable quantities, we shall 
have 

S = 51-55, 
pv = 630, 
wt;^ = 319; 

and resolving the equation with these values we find 

i; = 2519. 

Consequently, in fine, taking a mean between 25 
and 25*19, we have, for the definitive velocity 
sought, 

V = 25*10 miles per hour. 

Such then wiU be the velocity which the engine 
will assume, when drawing on a level a train of 
56 tons, tender included.- 



376 CHAPTER XII. 

2nd. To continue this example of the application 
of the formulae, let it he required to find what will 
be the velocity of the maximum useful effect of the 
engine. 

In order to effect this, we will replace in the 
equation proper to that problem, the pressure P 
in the boiler by its value P= 65 X 144=9360*6. 
per square foot ; and supposing first that the vapor- 
ization of the engine will undergo no change not- 
withstanding the reduction of velocity, we obtain 
the result 

,,> _ 1-804 X 48-75 1 ,.,« 

^ - 1-421 -h 0023 X 9360 ':2287=^^^^- 

This would then be the velocity sought, if the vapor- 
ization of the engine were invariable ; but as the 
diminution of velocity will lower the vaporization, 
which is such as we have supposed it, only at the 
velocity of 20 miles per hour, we will try whether 
the velocity of 16 miles will suit the formula. 
Then the effective vaporization of the engine, re- 
duced in the proportion of the fourth roots of the 
velocities, will become 46' 10 cubic feet of water 
per hour, and the formula resolved according to 
this supposition, will give 

v' = 16*20 miles per hour. 

This is therefore the velocity suitable to the pro- 
duction of the maximum useful effect required. 

3rd. In fine, to obtain the load corresponding to 
the maximum of useful effect, we recur to the proper 
equation, which is 



I 
I 

I 
I 

! 
I 
I 
I 
I 



PRACTICAL FORMULA. ' 377 

^ =-5-60+1) ^^-^^*^-^*^-6(T+F)"-6- ' 

and first calculating in this all the termSi except the 
last, we have as a result 

208-46. 

It remains then to subtract from this number 

•Iff * 
the value of -^-» to conclude from it definitively 

the required value of the load. As the value of 
the term 



depends on the number of carriages in the train, 
which will itself be known only by the definitive 
solution of the problem, we wiU again in this place 
follow the method of approximations. Supposing 
the load to be of about 160 tons, the train will 
consist of 31 carriages besides the tender; thus 
the efiective surface offered to the shock of the 
air, will be 

X = 70 + 33 X 10 = 400 square feet. 

Consequently the resistance of the air, at the velocity 
found, of 1 6'20 miles per hour, will be uv' ^=282 lbs., 
which gives 

^=4700; 

substituting then this valuation in the formula, we 
obtain the result 



378 CHAPTER XII. • 

M' = 208-46 ^ 4700 = 161-46. 

Consequently the load of 161*5 tons, forming a 
train of 31 carriages, besides the tender, will be 
the maximum load required. 

4th. In fine, if it be desired to know the maxi- 
mum velocity the engine is capable of attaining, 
when followed by its tender only, and without 
drawing any train, the proceeding will be as in 
the first case; but supposing the load to be of 
6 tons only, and taking account of the increase 
of vaporization, according to the velocity, the re- 
sult will be 

r = 35*03 miles per hour. 

In this last case, the useful efiect of the engine, 
tender not included^ will be null. 

From these detailed examples is seen how the 
calculation is to be performed in all the cases; 
but it must be remarked, that with the use of 
logarithms, these different trials present no sort 
of difficulty, and that those who have once got 
the habit of these researches, guess immediately 
and at a glance, what numbers they ought to 
employ in the approximations, so that the apparent 
length of the calculation entirely disappears. 

Collecting the results which we have just ob- 
tained, calculating moreover the useful effect of 
the engine, and expressing it under the different 
forms already indicated, we form the following 
Table : 



PRACTICAL FORMULiE. 379 

Effects of a locomotive of 65 cubic feet of vaporizatiouy 
with a had of 56 torn gross, on a level, tender included. 

M =56 tons g^oss, tender included, (10 car- 
riages and the tender) ; 

i; = 25*10 miles per hour; 

u. £ = 1411 tons gross drawn 1 mile per hour, 

tender included ; 

u. E. in HP. . . = 23 horses ; 

Q. CO. pr. t. pr. m. = '47 fb. per ton g^oss per mile, tender not 

included ; 

Q. wa. pr. t. pr. m. = *052 cuhic foot per ton g^oss per mile, 

tender not included ; 

u. E. 1 ft. CO. . . = 2*36 tons gross drawn 1 mile, tender in- 
cluded ; 

u. £. 1 ft. wa. . .= 21*70 tons gross drawn 1 mile, tender 

included ; 

Q. CO. fr. 1 HP. . = 26-60 fts. ; 

Q. wa. fr. 1 HP. . = 2-880 cubic feet; 

u. E. 1 ft. CO. in HP.= *038 horse ; 

u. E. 1 ft. wa. in HP.= '347 horse. 

Maxima effects of the same engine. 

M' =161*5 tons gross, tender included (31 

carriages and tender) ; 

v', = 16*20 miles per hour; 

u. E =2616 tons gross drawn 1 mile per hour, 

tender included ; 

u. E. in HP. . . = 42 horses ; 

Q. CO. pr. t. pr. ra. = *24 ft. per ton gross per mile, tender not 

included ; 

Q. wa. pr. t. pr. m. = '026 cubic foot per ton gross per mile, 

tender not included ; 

u. E. 1 ft. CO. . . =4*38 tons g^oss drawn 1 mile, tender in- 
cluded ; 



380 CHAPTBR XII. 



m E. I ft. wa. . . = 40'25 tons groes dnwn 1 mile, tender 

indoded; 
Q. CO. fir. 1 HP. . = 14-29 ■». 
Q. wa. fir. 1 HP. . = 1553 cubic foot; 
u. £. 1 ft. CO. in HP.= '070 hone ; 
n. £. 1 ft. wa. in HP.= *644 hone. 

To give a second example of this calculation, we 
will suppose the railway to have 7 feet of width of 
way, like the Great Western Railway^ and seek what 
will be the velocity of the engines of medium force, 
in use on that line, under the same circumstances 
as we have just examined relatively to a railway 
of about 5 feet of width of way. 

We will suppose then a locomotive of 120 cubic 
feet of vaporization, at the velocity of 25 miles per 
hour, with the following proportions: cylinders 14 
inches or 1*17 foot in diameter, stroke of the piston 
16 inches or 1*33 foot, wheels 8 feet in diameter, 
not coupled, weight 18 tons, friction 270 fts., blast- 
pipe 3*14 inches in diameter, total or absolute 
pressure in the boiler 80 lbs. per square inch, and 
consumption of coke in the same time 1050fts. or 
8*75 lbs. per cubic foot of water vaporized. More- 
over, by reason of the width of the way, we will take 
the surface of the largest waggon of the train at 100 
square feet, the average surface of a waggon at 56 
square feet, and the weight of the tender at 10 tons. 

Seeking then by the same calculation as before, 
what effects this engine is capable of producing, first 
in drawing a train of 60 tons gross, tender included, 



PRACTICAL FORMULiE. 381 

which makes 50 tons without the tender, and after- 
wards in drawing its maximum load, we obtain the 
following results : 



Effects of a locomotive of \20 cubic feet of vaporization^ 
with a load of^O tons gross, tender included* 

M =5 60 tons gross, tender induded (7 car- 
riages and the tender) ; 
V = 34*75 miles per hour; 

a. £ = 20S5 tons gross drawn 1 mile per hour, 

tender induded ; 

n. £. in HP. . . =: 33 horses ; 

Q. GO. pr. t. pr. m. = *60ft. per ton gross per mile, tender nai 

induded ; 

Q. wa. pr. t. pr. m. =: *069 cubic foot per ton gross per mile, 

tender not induded ; 

n. £. 1 ft. CO. . • = 1*99 ton gross drawn 1 mile, tender in- 
duded; 

u. £. 1 ft. wa. . . = 17'38 tons gross drawn 1 mile, tender 

included : 

Q. CO. fr. 1 HP. . = 31-48 tts. ; 

Q. wa. fr. 1 HP. . = 3-597 cubic feet ; 

u. £. 1 lb. CO. in HP.= -032 horse ; 

tt. £. 1 ft. wa. in HP.=: -278 horse. 



Maxima effects of the same engine. 

M' = 147 tons gross, tender induded (20 car- 
riages and the tender) ; 

v' = 25*55 miles per hour; 

u. £ = 3756 tons gross drawn 1 mile per hour, 

tender included ; 

Q. £. in HP, . . = 60 horses ; 



382 CHAPTER XII. 

Q. 00. pr. t. pr. m. = *301b. per ton grom per mile, tender moi 

mdiided; 

Q. wa. pr. t. pr. m. = '034 cubic foot per ton gross per mfle, 

tender moi indnded ; 

n. £. 1 ft. CO. . . = 3*58 tons giosB drswn 1 mile, tender in- 
dnded; 

n. E. 1 ft. wa. . . = 31'30 tons gross drawn 1 mik, tender 

indnded ; 

Q. CO. fir. 1 HP. . = 17-47*8. ; 

Q. wa. fir. 1 HP. . = 1997 cabic foot ; 

n. E. 1 ft. CO. in HP.= *057 horse; 

n. £. 1 ft. wa. in HP.= -501 horse. 

The velocity of the same engine, drawing its 
tender alone, would be 43*28 miles per hour; 
which would be the maximum of velocity that this 
engine could attain. 

It is visible, in these examples, that the above 
formulae present no difficulty, and that it is merely 
necessary to preserve in them the homogeneity of 
the measures employed. 



ARTICLE IV. 

BXPBBIMBNTS ON THB VBLOCITY ANd LOAD OP THB 

ENGINES. 

That a precise idea may be formed of the degree 
of accuracy attainable by the formulae which we have 
just given, and that besides, in case of need, calcu- 
lations may be grounded on material facts, we will 
here give a series of experiments, which we under- 



PRACTICAL FORMULiE. 383 

took with a view to know the velocities at which the 
engines draw different loads, in their ordinary and 
regular work. 

These experiments were made on the Manchester 
and Liverpool Bailway, of which this is the section, 
such as it results from a survey made in the month 
of August, 1833, by Mr. J. Dixon, then engineer to 
the Company. We give only that part of it which 
is traversed by the locomotives. There are besides, 
under the town of Liverpool, three tunnels, worked 
by stationary engines. 

The railway beginning at the Liverpool station, 
and ending at that of Manchester, traverses the 
following distances and inclinations : 

'53 mile, level. 

5*23 — descent nrffT 

1*47 — ascent ^ 

1-87 — level. 

r39 — descent -^ 

2'41 — descent ttVt 

6*60 — descent -^^ 

5'62 — ascent t^W 

4-36 — ascent TaVr 



29*48 miles. 



During the experiments in question, the .velocities 
were carefully taken by noting, in minutes and 
seconds, the moment of passing by every quarter of 
a mile on the road. The quarter miles are marked 
by numbered posts. At the same moment the 



1 



384 CHAPTER XII. 

pressure of the steam in the hoiler and in the blast- 
pipe was also observed. 

The weight of the waggons was taken exactly, in 
tons, hundred-weights, and pounds ; but we express 
it, for greater convenience, in tons and dedmals of a 
ton. The tenders of the engines were not weighed ; 
they are quoted at their average weight during 
the trip ; namely, 5*5 tons when water is taken on 
the road, and only 5 tons when that is not the case. 
The carriages containing passengers could not be 
weighed, because the regulations of the railway do 
not admit of that delay ; but we have here inserted 
their average weight, as well as that of the private 
carriages and trucks. 

The state of the weather is noted, because it is 
well known that a wind a-head, and, above aU, a side 
wind, which presses the flange of the wheels against 
the rails, increases the resistance of the train ; and 
the date of each experiment is given as a point of 
verification. 

The following Table contains the results of these 
experiments. The first column gives the description 
of the engine and its load, the second indicates 
the inclination of the portion of road traversed by 
the train, the third and fourth show the effective 
pressure of the steam in the boiler and in the blast- 
pipe, such as they were observed at the moment of 
the experiment. In the fifth we have given the 
opening of the regulator at the time, as a fracticm 



PRACTICAL FORMULA. 385 

of its total size; but it must be added that the 
engine Star, on which we had caused graduated 
divisions to be marked, was the only one which 
admitted of measuring the opening with precision. 
In the other engines, the handle of the regulator did 
not turn on a graduated circle, and therefore we 
could only set down the degree of the opening as it 
might be estimated by the eye. The sixth column 
of the Table contains the velocity of the engine, 
such as it was observed, and, in fine, the following 
column gives the result of our formula for the case 
considered. 

To perform the calculation relative to each en- 
gine, we use the determinations developed Chap. X. 
Thus we attend to the variation of the vaporization 
with the velocity of the motion, according to what 
has been indicated. We take account of the habitual 
blowing of the safety-valves during the progress, for 
all the engines, except the Star, which was not 
liable to such loss ; and it will be recollected that 
this loss amounts on an average to *05 of the total 
vaporization of the boiler. In the experiments 
made on the inclined planes, we likewise deduce 
the considerable loss which then manifests itself at 
the valves of all the engines, and of which the 
valuation has been seen for every case. We take 
account too of the water carried away with the 
steam without being vaporized, or, according to the 
technical term, the prime water; and for these 
divers dements of calculation, we refer to the 

2c 



386 CHAPTER XII. 

details oontained in Chapter X., without repeating 
here, for each engine, the determination which 
concerns it. Relatively to the absolute size of 
the regulator of the engines, we refer likewise to 
the chapter where that subject will be specially 
treated; in that place will be found, for each en- 
gine, the dimensions of the steam-ways, and conse- 
quently of the orifice of the regulator when it is 
entirely open. But as the greater or less opening of 
the regulator has no other action than that of pro- 
ducing directly the blowing of the valve, or indirectly 
the reduction of vaporization in the boiler, and as 
the use we make of the effective vaporization in our 
formulse already comprehends those two efiects, we 
merely indicate, in the fifth column, the opening of 
the regulator, by a fraction of its total size ; which 
will suffice for the finding of its absolute size, should 
it appear necessary. Finally, all the engines worked 
with more or less lead of the slide^ which is a 
particular disposition that we shall treat of in 
Chapter XVI.; but as we shall then find that 
this lead was very slight, and as its efiects besides 
are already found comprised in the loss of water by 
priming^ such as we have determined it, we will 
avoid complicating our calculations with this ad- 
dition. We shall make an exception however in 
this respect for the engine Vesta, because, in that 
engine, the loss by priming had been determined 
for another lead of the slide than that at which 
it worked in the experiment which we are about 



PRACTICAL FORMULA. 387 

to relate. For this case then we shall take ac- 
count of the lead of the sUde as will be indicated 
Chap. XVI. 

In making the comparison between the observed 
and the calculated velocities, attention must be paid 
to several circumstances. 

1st. There is reason to believe that, when engines 
work at less pressure in the boiler, they are liable to 
less loss by priming. As, therefore, we have made 
use in this respect of the mean determination for 
each engine, it is in general to be expected that in 
the cases of low pressure, the calculated velocities 
will be found somewhat too small, and that, in the 
contrary case, they will be rather too great. 

2d. The direction of the wind must necessarily 
have some influence on the velocity of the train. 

3d. When the water contained in the tender is 
very hot, since its heat diminishes continually as the 
journey advances, it will most commonly happen 
that the engine will vaporize more water, and con- 
sequently assume a greater velocity at the beginning 
of the experiment than at the end of it. 

4th. The difierences arising fix)m the three pre- 
ceding circumstances, become easily compensated 
by the irregularities in the vaporization of the 
engine; and these are inevitable, as well from the 
greater or less attention of the engine-man, as on 
account of the sudden slackening which the vapor- 
ization is subject to, ev^ time it becomes necessary 
to heap up the fire or to refill the boiler. Thus, 



( 



388 CHAPTER XII. 

since the observed velocities result from the actual 
and variable vaporization of the boiler, whereas the 
calculated velocities are determined from the mean 
vaporization of the engine, supposed to be uniform 
throughout the trip, there must necessarily occur, 
from time to time, considerable differences between 
the calculation and the observation; but it will 
readily be perceived that these differ^ioes depend 
on the irregularities of the vaporization, on ob- 
serving that, in the same trip, the engine often 
assumes its greatest velocity at the moment when 
the gravity opposes the greatest resistance, or that 
two portions of the line, on which the gravity is 
sensibly the same, are traversed with velocities very 
difierent. However, were the experiment sufficiently 
prolonged, all these momentary irregularities would 
disappear almost entirely. 



PRACTICAL FORMULiE. 



389 



Eaperimenti an the velocity and the load of locomotive engines. 



Date of the experiment, md 

derignstioii of 

tiie engibe md its load. 



Stab. Cylinder 
Stroke . 
Wheel . 
Wei(^t 
Fire-box 
Tubes . 
Friction 



14 in. 

12 in. 
5ft. 

11-201. 

49*71 Bq. ft. 
279*18 sq. ft. 
176 lbs. 



IncUnatioD 

of 
the road. 



Stak, Ang. 10, 1836, from liver, 
to Man., with 12 wag. and 
tender, 43*65 tons. 

Gross yaporiz. per hour, 65*49 
cubic feet, at the mean ve- 
locity of 20*78 miles per 
hour. 

Diameter of blast-pipe, 2*36 in. 

Star, Aug. 13, 1836, from Man. 
to IiEver., with 9 wag. and 
tender, 48*48 tons. 

Gross vaponz. per hour, 62*83 
cubic feet, at the mean ve- 
locity of 18*79 miles per 
hour. 

Diameter of blast-pipe, 1*78 in. 



Stae, Aug. 11, 1836, from liver, 
to Man., with 12 wag. and 
tender, 59*84 tons. 

Gross vaporiz. per hour, 61*05 
£ahic feet, at the mean ve- 
locity of 18-32 miles per 
hour. 

Diameter of blast-pipe, 2*82 in. 

Stae, Aug. 11, 1836, fhnn Man. 
to Liver., with 9 waggons 
loaded, 6 waggons empty, 
and tender, 61*24 tons. 

Gross vaporiz. per hour, 65-50 
cubic feet, at the mean ve 
locity of 17*46 miles per 
hour. 

Diameter of blast-pipe, 1-26 in. 



. o 



Ob- 

•erved 

effectire 

prenure 

in the 

boUer. 



Ob. 
■erred 
effeetiTe 
prewure 
in the 
blaat- 
pipe. 



Ifee. per 
■q. ineh. 














30*0 
27*1 
18-0 
22*6 
20*2 



Ibe. per 
■q. inch. 



27*7 
26*0 
280 
23-8 
26-4 
30-0 



27*0 
20*5 
221 
32*7 
31*0 
24*3 



M 



Opening 
of the 
regu- 
lator, in 
a frac- 
tion of 
its total 
die. 



Ob- 

■erred 

rdoettjr, 

inmilea 

hour. 



4-8 
2*4 
1*8 
2*9 
2*2 



5-4 
5*0 
4*2 
3-4 
4-9 
6-0 



»» 

n 
n 

If 
f» 



If 
>f 



•5 
•5 
•6 
•5 
•5 



■5 
■5 
•5 



milea. 



23-64 
20-00 
2500 
20-69 
20*77 



Calculated 
Telocity, 
in milea 
perhoor. 



21*82 
23-53 
18*75 
19*20 
20*00 
20-00 



24*62 
16-67 
20-87 
22*50 
20*00 
18*00 



15-00 
21-43 
16*79 
18-75 



mOea. 



22-12 
21-88 
24-10 
20-14 
21-22 



Obaerrstiona. 



Weather fair and 

calm. 
Water in the ten 

der hot. 



20*82 
21*89 
18-83 
20*23 
19-66 
18-65 



22-00 
19-97 
20-85 
22-27 
18*77 
19*74 



Weather fair and 
cahn. 

Water in the ten 
der hot. 



rWeather fur and 

calm. 
Water in the ten 

der tepid. 



17*48 
18-91 
15-97 
17-00 



Weather hkt and 

aim. 
Water in the ten« 

der cold. 



390 



CHAPTER XII. 



Date of the ezpcrimeat, and 

thm <>n g w» ^ VoA its llWld 



iBdinatkm 



of 
the road. 



Stab, Aug. 9, 1836, firom Man. to 
Liver., with 3 wag. loaded, 
32 wag. empty, and tender, 
75*05 tons. 

Gross Taporiz. per hour, 68*79 
cubic feet, at the mean ve- 
locity of 14'45 miles per 
hour. 

Diameter of blast-pipe, 2 in. 



With 38*58 tons 
With 41-97 tons 



Stak, Aug. 9, 1836, from Liver, 
to ifan., with 20 wag. and 
tender, 96*30 tons. 

Gross vaporiz. per hour, 60*64 
cabic feet, at the mean ve 
locity of 17-35 nules per 
hoar. 

Diameter of blast-pipe, 2-82 in. 



Stae, Aug. 13, 1836, from liver, 
to Man., with 22 wag. and 
tender, 109*68 tons. 

Gross vaporiz. per hoar, 54*20 
cabic feet, at the mean ve- 
locity of 13-85 miles per 
hoar. 

Diameter of blast-pipe, 2 in. 



Stak, Aag. 9, 1836, from lAver. 
to Man., with 23 wag. and 
tender, 120-27 tons. 

GroM vaporiz. per hoar, 67*71 
cabic feet, at the mean ve- 
locity of 15*13 miles per 
hoar. 

Diameter of blast-pipe, 2 in. 



fta.per 
■q. laeh. 



*• vrn 
o 



^ A 
•• ^ 



42-3 
36-0 
30-0 



o 

d* tH, 

*" TWlfT 



Ob- 



iatke 
boOer. 



Ob. 

dibetive 



'Opening 
of the 



intlie 
Mart- 
pipe- 





*■ Xwsr 



o 

d. wH 

*■ unnr 



41*6 
42-5 
45-2 
48-6 
44-3 
481 



49-6 
50-6 



40*0 
31*5 



23*6 
38*8 
42*0 
30*7 
37-5 
330 



32*3 
480 
26*0 
39*8 
41*2 
450 



Die. per 
■q. inch. 



4*8 
5*1 
4*4 
5*8 
6*3 
6-2 






2*8 
1-8 



3*0 
2-4 
2*3 
1*8 
2-3 
2*0 



1-0 
2*4 
3-8 
2-1 
1-6 
1-2 



4*3 
50 
3*0 
5-6 
4-4 
4*9 



lator,in 



tion of 
its total 



1 
1 
1 
1 
1 
1 



1 
1 




nulci. 



16-96 
17-50 
14-53 
16-67 
16-39 
17-73 



911 
7-28 



22*85 
2000 
20*00 
21-82 
17-56 
19*25 



19*57 
13*33 
1714 
15-00 
12-63 
12*47 



16-95 
15*00 
1500 
17*21 
15-24 
16*55 



milei. 



19-03 
19-92 
16-47 
17*46 
18-30 
16-43 



10*27 
10-11 



Weather fur ind 
calm. 

I 

Water in the ten- 
der Teiybot. 



19-00 
17-00 
17*90 
20*10 
15*58 
16*75 



18*00 
14*38 
15*17 
18-09 
13*60 
14*84 



19-71 
16-87 
18-63 
19*45 
15*03 
16*08 



Weather frtr uJ 



in the fees- 
hot. 



Wenther fair aad, 



Water in the ftco 
dor cold. 



Weather lur aa^ 
I calm. 

^ Water in the ten- 
der almost cold. 



1 



PRACTICAL FORMULiG. 



391- 











Opening 














Ob- 


of the 












Ob- 


■enred 


rega- 


Ob- 










■erred 


effMliye 


lator,in 


•erred 


Calenlated 




Date o£ the experiment, and 




eflfiBctiTe 


preMure 


a tac- 


rdodty. 


▼eloeity. 




deaigiiiili<m of 


of 


prewuK 


in the 


tion of 


inmilet 


inndlea 


Obacrvatiooa. 


the engine and ita load. 


tberoad. 


in the 


blaat. 


ita total 


per 


per hour. 








boUer. 


pipe. 


aiie. 


hour. 










Ibe. per 


Ibe. per 




miles. 


miles. 








■q. inch. 












VxsTA. Cylmder . a 11*125 in. 
















Stroke ... 16 in. 
















Wheel ... 5 ft. 
















Weight... 8*71 1. 
Fire-hox . . 46*00 Bq. ft. 






























Tubes. . . 215-66 sq. ft. 
















Blast-pipe.. 2-50 in. 




• 












Friction.. 181 fbs. 
















Vesta, Aug. I, 1834, from Man. 


»- 










^ 




to Liver., with 5 waggons 


^WST 


50 


tr 




30*00 


30*60 


Weather fur. A 


loaded, 5 empty, and ten- 


"•TiAnr 


50 


tt 




34*74 


31-07 


moderate wind 


der, 33*15 tons. 


. *• ¥i¥ 


50 


n 




28*93 


29*09 


in favoor of the 


Gross vaporiz. per hour, 




55 


>f 




14-11 


15-50 ' 


motion. 


65-00 cubic feet, at the 





50 


n 




29*00 


30*18 


Water in tiie ten- 


mean velocity of 27*33 


•• Tihrf 


50 


tt 




28-80 


2911 


der Teiy hot. 


miles per hour. 


m 










.. 




FiRSFLT. Cylinder . 11 in. 
















Stroke . • 18 in. 














- 


Wheel .. 5 ft. 
















Weight . . 8-74 t. 
















Fhe-box . 43*91 sq. fl. 
















Tubes . 317*71 sq. ft. 
















Blast-pipe 2*25 in. 
















Friction 123 lbs. 
















FiRBFLT, July 26, 1834, from 


i» 














Liver, to Man., with 8 














Weather fiiir. 


first-dass coaches, and 





50 


ft 


1 


24*00 


25*09 


Water in the ten- 


tender, 41*40 tons. 


, ^lAt 


45 


M 


1 


25*45 


27*08 


The engine in a 


Gross vaporiz. per hour, 




45 


tt 


1 


21*29 


23*96 ' 


bad state, losing 


64*10 cubic feet, at the 


••tAt 


35 


tt 


1 


21*33 


24-48 


water by the 

tnli^ of th« 


mean f^odty of 17*70 














boiler. 


miles per hour. 


» 












Weather rainy. 


FiRBFLT, July 26, 1834, from 


«• 










— 


A rather strong 


Man. to liver., with 8 
first-dass coaches, and 
tender, 41*40 tons. 
Gross vaporiz. per hour, 
77*31 cubic feet, at the 
mean velocity of 21*33 





45 

50*33 

50*5 

50*33 

50 


tt 
tt 
tt 

tt 
tt 


•5 

•5 

•5 

5 

5 


23*68 
24-44 
23-44 
25*71 
24*82 


27-93 
28*56 
25*40 ^ 
26-59 
25*70 


wind against the 
direction of the 
motion. 

Water in the ten- 
der tepid. 

The engine in a 
bad state, losing 
water by the 


miles per hour. 


^ 










■• 


tubes of the 
boiler. 



392 



CHAPTER XII. 









• 


Opening 














Ob- 


of the 








• 




Ob- 


serred 


regn- 


Ob- 










serred 


effBClive 


Utor^in 


served 


Calculated 






Indinstion 


effective 


pressure 


afinie- 


relocity. 


yeloatir. 




designation of 


of 


pressure 


in the 


tionof 


in miles 


m milea 


OtiliiitiiiiiB 


the engine and its load. 


the rood. 


in the 


blast- 


iU total 


per 


perhovr. 


1 






boiler. 


pipe. 


siae. 


hour. 




1 






lbs. per 
■q. inch. 


lbs. per 
sq. Siidi. 




miles. 


miles. 


1 


FuBY. Cylinder . . 11 in. 














i 


Stroke . . . 


16 in. 














■ 


Wheel . . , 


5 ft. 










) 






Weight . . 


. 8-20 1. 
















Fire-box . . 


. 32*87 sq. ft. 
















Tubes . . 


. 267-84 sq. ft. 
















Blast-pipe . 


2-156 in. 
















Friction . . 


, 96tbs. 














' 


FtJBT, July 24, 1834, from Man. 
to Liver., with 10 wag. and 
tender, 48-80 tons. 
Gross vaporiz. per hour, 57*46 
cubic feet, at the mean ve- 
locity of 18*63 miles peri 
hour. 


d-rATT 



••tAtt 


55 
55 
55 
67 
55 
55 


n 
n 
n 
ff 
>i 


-75 
-75 
•75 
1 

•75 
•75 


21-43 
22-00 
18-62 
15-00 
17-50 
18^46 


20-73 ^ 
21-72 
18-57 
8-00 ' 
20-10 
18-80 


Weather feir. A 
rather sCroa; 
side wind St ia- 
tervals. 

Water in the tfi-i 
doreold. 

1 


Fury, July 24, 1834, from Liver, 
to Man., with 10 wag. and 
tender, 56-16 tons. 
Gross vaporiz. per hour, 54-45 
cubic feet, at the mean ve- 
locity of 19-67 miles per 
hour. 





55 

65-5 

55 

55 

55-5 

55 


n 

M 

n 

n 
ft 
n 


•75 
1 

•75 
•75 
•75 
•75 


1800 
6-31 
17-14 
23-28 
21-82 
2117 


20-14' 

6-74 
18-82 
20-50 ^ 
17-45 
18-07 


Weather fiurns 

Water in the to^ 
deroold. 

1 


Lbsdb. Cylinder . 11 in. 
















Stroke . . 16 in. 
















Wheel. . . 5 ft. 
















Weight . . 7-07 t. 
















Fire-box . . 34-57 sq. ft. 
















Tubes . . . 267-84 sq^ ft 
















Blast-pipe . 2-156 in. 










■ 


» 




Friction . . 85 lbs. 
















Lbbds, Aug. 15, 1834, from Liver. 


»• 










•< 




to Man., with 20 wag. and 
tender, 88-34 tons. 


^-rrfn 


54 


tt 


•75 


20-72 


22-26 




• ^^ ^ ^ 




54-75 


t» 


-75 


18-26 


20-25 


Weather calm. 


Gross vaporiz. per hour, 63-18 


* ^ rb 


54 


»f • 


-75 


24-00 


23-00 > 


Water in the tcB- 

S 1_ *A 


cubic feet, at the mean 


•- "nAnr 


54 


>f 


-75 


20-34 


19-00 


der scarcely tr- 
PW. 


velocity of 18*63 miles per 


^Wkt 


54 


f» 


•75 


18-82 


19-60 


hour. 




h> 








• 


^ 





PRACTICAL FORMULA. 



393 











Opening 














Ob- 


of the 












Ob- 


■erred 


regu. 


Ob- 










awed 


eflectiTe 


lator,in 


■erred 


Calenlated 




Date of Um eipcrisMot, and 
dwignatwia of 


f|^Hp>^^f^^ 


eflbcliTe 


in the 


afrae- 


velocity, 
in miles 


velocity, 
in milea 




ol 


preaauie 


tion of 


^^a » * 


the engine and ita load. 


Iheioad. 


in the 


blaat- 


ita total 


,P» 


per hour. 








bailer. 


pipe. 


■iae. 


hour. 










Iba. per 


Iba. per 




milea. 


milei. 








■q. inch. 


■qiindi. 










Lkbds, Aug. 15, 1834, from Mao. 


p" 










" 




to Liyer., with 8 wag. and 
















tender, 39-88 tons, half 


d.:iAT 


51-5 


»» 


-76 


24-54 


27*16 


Weather Ciir and 


the road, and 7 wag. and 


d-TiAnj 


46-5 


» 


•75 


30-00 


28-11 


calm. 


tender, 35-15 tons, &e reit 


, *• »*T 


46-5 


»» 


■75 


25-31 


25*25 


Water in the ten- 


of the way. 


4 — -w-^ 

O 


46-5 


fi 


-76 


22-50 


27-75 


der very hot. 


GroM Taporiz. per hour, 68-82 


•- ^ 


48-5 


»f 


I 


10-00 


14*97 


One wag. left be- 


cubic feet, at the mean 


•■ Tf^ 


54 


i> 


•75 


25-71 


26-20 


hind half way. 


▼elodty of 21-99 miles pei 
















hour. 


>. 










a 




Vu LC AN. - Cylinder 1 1 in. 
















Stroke . . 16 in. 
















Wheel • . & ft. 
















Weight . 8-34 t 
















Fire-box 34*45 sq. ft 
















Tubes . . 267-84 sq. ft. 
















Blast-pipe 2-156 in. 
















Friction . 125 ibs. 
















Vulcan, July 22, 1834, from Man. 


>» 










^ 




to Uver., with 9 first- 
















dass coaches and tender, 
















39-07 tons. 
Gross Tiq^riz. per hour, 
60*60 cubic feet, at the 


• •• A 


57-5 

• 


»f 


1 


11-42 


11-22 ' 


Weather calm. 

Water in the tm- 
der hardly tq>id. 


mean velocity of 22*99 
















miles per hour. 


>• 










■^ 




Atuws. Cylinder . 12 in. 
















Stroke . . 16 in. 
















Wheel ... 5 ft. 
















Weight . . 11-40 t. 
















Fire-box . 57-07 sq. ft. 
















Tubes . . . 197-25 sq. ft. 
















Friction . . 139 ibs. 
















Atlas, July 23, 1834, fix>m Liver, 
to Man., with 40 wag. and 
tender, 195-5 tons. 


o 


53 
53-5 


M 




14-12 
9-23 


13-50 
10-05 


Weather feir and 
calm. 

Water in the ten- 


Gross Taporiz. per hour, 43-81 
cubic feet, at the mean ve- 
locity of 8*99 miles per 
hour. 




53 
55 
54*5 


ft 

rf 
»> 




16-21 
800 
5-87 


14-00 ^ 
8-38 
9-60 


der cold. 

The encine was 
assisted at start- 
ing by two other 


BUst-pipe, 2-94 in. 


>. 










- 


engines. 



396 CHAPTER Xlll. 

the engine with an indeterminate load or velocity, 
and the two others to the production of the max- 
imum of useful effect. 

From hence then it results that, according as 
either of these general analogies he taken to deter- 
mine one or other of the dimensions of the engine, 
the following are the questions that it may be pro^ 
posed to resolve : 

« 

1st. To determine, either the heating surface of the 
boiler, or the diameter of the cylinder, or the 
length of the stroke of the piston, or the diameter 
of the wheel, that the engine may draw a given 
load at a desired velocity ; 

2d. To determine, either the heating surface of the 
boiler, or the diameter of the cylinder, or the 
stroke of the piston, or the diameter of the wheel, 
or, in fine, the pressure in the boiler, that the 
engine may acquire a desired velocity, or draw 
a given load, producing at the same time its 
maximum of useful effect ; 

3d. To determine the combined proportions proper 
to be given to the divers parts of the engine, to 
enable the engine to fulfil divers simultaneous 
conditions. 

Each of these three enunciati<m8 visibly compre- 
hends a series of distinct questions, which we shall 
resolve successively. We shall therefore first suppose 
that it is required to determine one of the dimensions 
of the engine, according to the general condition of 



CHAPTER Xm. 

OF THE PROPORTIONS OF LOCOMOTIVE ENGINES. 

Sbct. I. Of the divers problems which occur in the 
construction of locomotive engines. 

In the preceding chapter, we have sought the effects 
producible by a locomotive engine already con- 
structed, or whose dimensions are determined; we 
are now about to determine, on the contrary, what 
should be the proportions of a locomotive engine, 
as yet unbuilt, in order to obtain from it desired 
effects. 

In this state of the question, the quantities given 
h priori are the load of the engine for a known 
velocity, or else its velocity or its load corresponding 
to the maximum of useful effect ; and the unknown 
or indeterminate quantities are the heating surface 
of the boiler, the diameter of the cylinder, the length 
of the stroke, the diameter of the wheel, and the 
pressure in the boiler. 

On the other hand, we have demonstrated in the 
preceding chapter, that there exist between these 
divers quantities, known or unknown, three general 
analogies expressed by the equations (1 bis), (4 bis), 
and (5); the first relating to the general effects of 



398 CHAPTER XIII. 

Substituting then in this equation for v and M, the 
given velocity and load, putting likewise, for the 
dimensions of the engine, their values which may 
be taken arbitrarily, and, in fine, putting for F the 
presumed friction of the engine, such as we have 
given the means of valuing it in Chapter VIII., we 
shall obtain the effective vaporization which the en- 
gine ought to have, in order to fulfil the condition 
prescribed. 

Thence must afterwards be deduced the total or 
gross vaporization of the boiler. Now we have 
found that in locomotive engines of the present 
construction, the efiective vaporization is to the 
total vaporization in the ratio of the numbers '75 
and 1. Therefore the total vaporization of water, 
corresponding to the efiective vaporization S, is 

S'= A= 1-33 S. 
•75 

And as moreover, in certain engines, there is yet 
lost, during the motion and by the safety-valves, 
^ of the total water vaporized, it follows that for 
those engines, we shall have the definitive total 
vaporization of the boiler, on multiplying the 
quantity just obtained by the factor 1 '05 ; so that 
the total vaporization will then be 

S'=1'05X 1-33 S= 1-40 S. 

Thus will then be attained the knowledge of the 
total vaporization necessary to the production of the 
desired efiects. This vaporization will be such as 



OF THE PROPORTfONS OF THE ENGINES. 399 

the engine ought to produce at the given velocity v, 
and since we have seen that the vaporization varies 
in the ratio of the fourth roots of the velocities, it 
follows that at the velocity of 20 miles per hour, 
the same engine ought to be capable of vaporizing a 
quantity of water expressed by 

1-40 SX(^)*- 

Consequently, if it be desired to conclude from 
hence the heating surface which the boiler ought 
to have, it will suffice to refer to the results which 
we have obtained in Chapter X., namely: that at 
the velocity of 20 miles per hour, each square foot 
of total heating surface produces a vaporization of 
•200 cubic foot of water per hour. Thus the total 
heating surface necessary to produce the effective 
vaporization S, at the given velocity v, will be 

•20 V t; / V v / 

If the given velocity v differ but little from 20 
miles per hour, or if a very great degree of precision 
is not required, we may, in this expression, neglect 
the term 

and be satisfied with taking the heating surface 
equal to the quantity 7S. 

It appears at the same time that, in order to 
obtain immediately the effective vaporization of a 



400 CHAPTBR XIII. 

given boiler, we may limit the calcalation to taking 
i|^ of the total heating surface, exin'essed in square 
feet; and the result will he the vaporization ex- 
pressed in cubic feet of water per hour. This sum- 
mary method may be used in practice, as an ap- 
proximation. 



Sect. III. Of the diameter of the cylinders^ necessary 
that the engine may draw a given load at a given 
velocity. 

K, in planning an engine, the vaporization which 
the boiler is to have has been previously settled, 
desired effects may yet be attained by 



for that purpose one of the other dimaisions of the 
engine. 

For instance, the diameter of the cylinders, which 
would enable the engine to fulfil the prescribed con- 
ditions, may be sought. To obtain the solution of 
this problem, it evidently suffices to solve equation 
(1 bis) with reference to d, which is the diameter of 
the cylinder, and we have 



^ D i + « 



9 



C5So-frc-(-r^-(*±'>"^'"— '-i^ - w 



Substituting in this equation, for S, v, M, D and 
/, the values that have been previously fixed on, 
introducing for F the presumed fiiction of the 
aigine, such as we have found it in Chapter VIII., 
and for pv the pressure in the blast-pipe, resulting 



OF THE PROPORTIONS OF THE ENGINES. 401 

from the proportions adopted, we shall obtain in the 
second member the value of d^, taking the square 
root of which we have definitively the value of rf, 
or the diameter of the cylinder expressed in feet. 

It is to be remarked that the proposed problem 
will be possible only when 

5280-/— cTTT»-7>(*±^)^±^^-^'-^TT5-' 



or 



S >5280 ^(1 + «)^ [](*±^)M±^ + i«r 2+ j-|y] ; 



for otherwise the second member of the equation 
would become negative, and the value of d would 
be imaginary. This condition is readily explained 
on referring to the general value of the vaporization 
necessary to draw the load M at the velocity v. 
This general value is, as has been seen, according 
to equation (7), 



5280 



and it is manifest, on the mere inspection, that if 
the value supposed for S did not fulfil the condition 
indicated above, the vaporization would be. insuf- 
ficient to draw the load M at the velocity v, what- 
ever might be the diameter chosen for the cylinder. 
The impossibility of the problem would arise then 
from the values adopted for S, M and v being in- 
compatible with each other; but on taking a suf- 
ficient value for S, the required solution will be 
easily attained, by me^ns of the preceding formula. 

2 D 



402 CHAPTER xni. 



Sect. IV. Of the length of the stroke of the piston^ 
requisite for the engine to draw a given load ai a 
given velocity. 

If, besides the vaporization of the boiler, the 
diameter of the cylinder has also been fixed upon, 
but that nothing has been decided relative to the 
stroke of the piston, the value of this undetermined 
quantity may still be obtained, such as to enable 
the engine to fulfil the desired conditions. 

To obtain the length of stroke proper for an 
engine, entirely determined in other respects, in 
order that it may draw a desired load at a given 
velocity, it will be sufficient to resolve equation 
(1 bis) with reference to /, which will give 

9 

This equation then will solve the question, and it 
will be remarked that, to prevent I from becoming 
a negative quantity, the value of S must fulfil the 
same condition as in the preceding inquiry, which 
is explained in the same manner. 

The presumed friction F of the engine, and the 
pressure p'v in the blast-pipe, which are to be sub- 
stituted in the equation, will be obtained as it has 
been said in the last section. 



OF THE PROPORTIONS OF THE ENGINES. 403 



Sect. V. Of the diameter of the wheels necessary 
far the engine to attain a desired velocity with 
a given load. 

In fine, it may still occur that from different 
considerations all the other proportions of the en- 
gine have been decided on, and that with these 
proportions it be required to know, what diameter 
should be given to the propelling wheel of the 
engine, that it may acquire a desired velocity with 
a ^ven load. 

The quantity D in this case becomes the object of 
determination of the problem, and its value will 
again be drawn from equation (1 bis), namely : 

^-ITi--r-T-T-T-4-— —Z — T--W 



5280 ' 



/rc-7-Tn-ir-(*±^>^+^-""'-TT? 



It will be remarked that this equation, like the 
two preceding ones, is also subject to the condition 
that the vaporization adopted for the engine be not 
incompatible with the load and the velocity which 
are intended for it at the same time; and it is, of 
course, needless to add, that if the value of D re- 
sulting from this formula should be found too large 
or too small to be applicable in practice, the solution 
obtained must be regarded merely as satisfying the 
algebraic equation, but by no means as solving the 
practical problem in the manner it ought to be 
understood. 



404 CHAPTER XIII. 



Sect. VI. Of the vaporization^ or of the heating 
surface a locomotive engine ought to have^ in order 
to acquire a given velocity, producing at the same 
time its maximum of useful effect. 

The four questions which have occupied us thus 
far, have had in view to determine one or other 
of the dimensions of the engine, from equation 
(1 bis), that is, from the condition that the engine 
draw any given load whatever, at a given velocity. 
But we are now about to suppose that it is required 
to determine the dimensions of the engine, not from 
its effects with any given load, but from the con- 
dition that it produce its maximum usefrd effect, 
either at a given velocity, or with a given load; 
and as the relation between the dimensions of the 
engine and its maxima effects is expressed by the 
two equations (4 bis) and (5) , namely : 

,^ JL s^ D I 

^ *5280 • rf« • /+c 'fi + yP' 

to these we must have recourse in order to attain 
the solution sought. 

Suppose, then, it be required to determine the 
vaporization S, or, in other words, the heating 
surface of the engine, according to the conditiqn 
that it produce its maximum of usefrd effect at a 
certain given velocity v\ 



OF THE PROPORTIONS OF THE ENGINES. 405 

It is clear, then, that the value of S must he 
derived from equation (4 bis) , which will give 

S=5280 L±l , ^' . ^' (" -f P) ..... (11) 
/ D \q ' 

This equation will make known the effective vapor- 
ization sought, as soon as v and the dimensions 
of the engine shall be replaced by their values 
supposed fixed or chosen beforehand; and from 
it will be concluded, as in Sect. i. of this chapter, 
the total consumption of water in the boiler, and 
consequently the heating surface necessary to obtain 
the desired effect. 

It will be remarked that, as equation (5) furnishes 
no relation between the vaporization S and the 
maximum load of the engine, the vaporization can- 
not be determined directly, from the condition of 
the engine drawing a certain given load, producing 
at the same time its maximum useful effect. It is 
evident, indeed, that as this condition depends 
entirely on the effort the engine is capable of ex- 
erting, and is altogether independent of the velocity 
of the motion, the question is to be solved only by 
seeking the pressure of the steam in the boiler, 
capable of producing the determined effort; and 
consequently it is in the next problem that its solu- 
tion win be found. 



406 CHAPTER XIII. 



Sect. VII. Of the pressure in the boiler necessary 
for the engine to draw a given load^ or acquire a 
desired velocity^ producing at the same Hme its 
maximuta of useful effect. 

If the maximum load of the engine, or, in other 
words, the load it should draw when producing its 
maximum of useful effect, have been previously 
decided on, and if it be desired to know what 
ought to be the pressure in the boiler, to enable the 
engine to draw that maximum load, it is clearly to 
equation (5) that recourse must be had, since that 
is precisely the equation which gives the relation 
between the known and unknown quantities of the 
problem under consideration. 

Resolving then this equation with reference to P, 
which is the pressure in the boiler, we obtain 

This formula then will make known the pressure P. 
It is to be observed only that this equation con- 
tains two terms pv and uv^^ functions of the 
minimum velocity of the engine, which is not given 
h priori^ but which is, on the contrary, to result 
from the knowledge of P, according to the equation 
(1 bis), when that quantity P shall be determined. 
This circumstance therefore will render it necessary 
to operate here in the same manner as we have 
already indicated relatively to equation (1), in the 



OF THB PR0P0ETJ0N8 OF THE ENGINES. 407 

preceding chapter; that is to say, the operation 
must be performed by successive approximations. 
A supposition therefore must first be made as to the 
probable value of tr\ and having calculated, with that 
supposition, the value of P, it must be ascertained, 
by seeking the velocity of maximum useful effect for 
the pressure P and the known vaporization S of the 
engine, whether that vdocity be too remote from 
that whidi was supposed for the finding of P. If 
the difference between the two is trifling, this first 
solution will suffice, and the value thus obtained for 
P may be adopted. If, on the contrary, th^ velocity 
of maximum useful effect, resulting from the values 
of P and S, differ from the supposition originally 
made, too much to warrant placing confidence in the 
result, then the calculation must be begun anew, 
introducing into the equation (12) the velocity v ob- 
tained by this first approximation, and thence will be 
deduced a new value of P more approximate than the 
first. This would lead, if required, to a third ap- 
proximation ; but with a little experience, two trials 
will always lead to a value of P sufficiently near for 
practical uses. The problem therefore may be 
somewhat long to s(dve, but can present no sort of 
difficulty. 

The solution thus obtained will give the total or 
absolute pressure of the steam in the boiler, ex- 
pressed in pounds per square foot; that is, ex- 
pressed generally in units of the species of those 
which are determined by the homogeneity of the 



408 CHAPTER XIII. 

equations, as has been explained in Sect iv. of the 
preceding chapter. 

Instead of determining the pressure in the boiler, 
as we have just done it, that is, according to the con- 
dition that the engine draw a given load, producing 
at the same time its maximum of useful effect, we 
may likewise determine that pressure, according 
to the condition that the engine shall, with a iSxed 
vaporization, attain a certain given velocity, pro- 
ducing also its maximum of useful effect. 

It will then be from equation (4 bis) that the 
value of P must be drawn, which gives 

5280 ' q ' l+c' d^r f/ q ^ ^ 

And substituting in this equation the value of the 
divers dimensions of the engine, we have the 
pressure in the boiler, which, for a given vapor- 
ization, will make the engine assume the desired 
velocity v\ producing at the same time its maximum 
useful effect. 



Sect. VIII. Of the diameter of the cylinder^ or of 
the stroke of the piston^ or of the diameter of the 
wheels necessary that an engine may assume a 
desired velocity or draw a given loady producing 
also its maximum useful effect. 

It has been seen in the two preceding problems, 
that if the engine is required to assume a given 



OF THE PROPORTIONS OF THE ENGINES. 409 

vdocity, producing at the same time its maximum 
of useful eflfect, there are two ways of attaining that 
»xd : either by determining the vaporization neces- 
sary for the producing of that effect, or by assuming 
any vaporization, and then determining the pressure 
in the boiler proper to obtain the desired velocity. 

We have just seen likewise, that if it be wished to 
render the engine capable of drawing a certain given 
maximum load, that end may be attained by deter- 
mining, from equation (12), the pressure which 
ought then to be produced in the boiler. 

But besides these means of attaining the desired 
effects, there are yet three other ways, which consist 
in adopting arbitrarily the vaporization of the engine 
and the pressure in the boiler, and then determining 
either the diameter of the cylinder, or the stroke of 
the piston, or the diameter of the wheel, according 
to the condition proposed to be fulfilled. 

Suppose then that the vaporization of the engine 
and the pressure of the boiler be already fixed by 
other considerations, and that it be required of the 
engine to produce its maximum useful effect at a 
certain fixed velocity v. Then it will clearly suffice to 
resolve the equation (4 bis) with reference to d, to /, 
or to D, according to which of those three quantities 
it is wished to determine from that condition. We 
shall have then 

"^ -5280 • /+c • J • r ^' ^7^' • • • • ^*^^ 

or 



410 CHAPTBB XIII. 

,_ 1 /IDS 1 „.v 

6280 /+c .^ rf» t/ «^p ^ ^ 



or , 



D=528oLtf . jd2/. ^ . (- + P) (16) 

We may therefore choose one of these three solu- 
tions ; and introducing into the equations for S, P, 
and the dimensions of the engine, their values pre- 
viously decided on, we shall obtain the value of 
those dimensions which shall have been left to 
determine according to the prescribed condition. 

If, instead of laying down the condition th&t the 
engine acquire the velocity v producing also its 
maximiun useful effect, we, on the contrary, impose 
the condition that it draw a certain given maximum 
load M^, then the problem will be the same as the 
preceding, with the exception that M' will be given 
instead of v. Kecourse therefore will be had to 
equation (5), which, resolved successively with refer- 
ence to (2, I and D, will give 

or 

F 



(k±g)ye±gm'^m/^+ 



or, in fine, 

JJ— j—r . = . . . (i»; 

1+* 



OF THB PROPORTIONS OF THE ENGINES. 411 



As these equations still contain the terms f^v and 
uv"^^ which are functions of the velocity v\ and as 
the latter is not yet known, but must on the 
contrary result from the previous knowledge of d, I 
or Dy the proceeding here will be by successive 
approximations, as we have indicated above, in 
Sect VII. 



Sect. EX. Of the combined proportions to be given 
to the parts of an engine, to enal}le it to fulfil 
divers simultaneotLS conditions. 

In all the preceding problems we have supposed 
that all the dimensions of the engine, except one, are 
assumed at will, and that this one dimension is 
afterwards determined according to some condition 
imposed as to the work of the engine. But as in 
the general problem of the constructicm of an 
engine, there are five indeterminate quantities, 
namely: the heating suifaoe, or, in other words, 
the vaporization, the pressure in the boiler, the 
diameter of the cylinder, the length of the stroke of 
the piston, and the diameter of the wheel, it is 
evident that five simultaneous conditions may be 
prescribed, for the engine to fulfil, and that on 
determining each of the said dimensions according 
to those conditions, the engine will be capable of 
fulfilling them all successively, according to the 
circumstances in which it is placed. 

The conditions that may be prescribed, to deter- 



412 CHAPTER XIII. 

mine the dimensions of the divers' parts of the 
engine, consist in fixing the different effects it 
ought to produce under certain circumstances ; and 
these effects themselves depend on three quantities 
that may be assumed at will; namely, the velocity for 
any given load whatever, the velocity of maximum 
useful effect, and the maximum load, or load of 
maximum useful effect. 

As many as five values then of these different 
quantities may be assumed, and the five dimensions 
of the engine may be determined according to them ; 
or four only of those values may be assumed, and 
four of the dimensions of the engine determined 
from them, the fifth then remaining to be chosen 
arbitrarily; or, in fine, three or two, or even one only 
of those conditions may be assumed, and the same 
number of dimensions determined, the others re- 
maining either to be taken arbitrarily or to be de- 
termined from considerations of a different nature. 

It is obvious that a considerable number of 
problems may be proposed on this subject; but 
they never present any difficulty. It will suffice, 
in effect, to recur to equations (1 bis), (4 bis), and 
(5), and to express that they exist at the same 
time, for the given values of the quantities M, t;, 
M', v\ Then will be drawn firom them, by elimina- 
tion, the value of each of the required dimensions of 
the engine. 

We will not undertake to solve all the problems 
that may be thus proposed ; but to show the manner 



OF THE PROPORTIONS OF THE ENGINES. 413 

of the proceeding, we will choose one or two among 
those which may occur most frequently. 

Suppose it be desired to build an engine capable 
of drawing, on a given inclination, a certain deter- 
mined maximum load M^ and, at the same time, of 
acquiring on another inclination, a certain given 
velocity v, with another load M likewise known. 

We have then at the same time the two equations 
(4 bis) and (1 bis), or 

M'=- - — l!i — --(p-^-yt,') - i- /_!_-+ tii,'«+^\, 



These may, consequently, be used to determine, for 
instance, the diameter of the cylinder from the first 
condition, and the heating surface from the second. 
The first equation therefore must be resolved with 
reference to d, and the second with reference to S. 
This is what we have already done in the Sections 
VIII. and II., having obtained the equations (17) 
and (7), namely: 

^-(^^»>7- V^p^p'^ (l^T) 

S-5280^%(l + 8)^[(*±^)M±^ + iii^+-jl^+^.^(»+p+y^)].^^ 

Thus, introducing into equation (17), the given 
value for M', we first deduce the value of d, as 
has been explained Sect. viii. ; and then sub- 



404 CHAPTER XIII. 



Sect, VI. Of the vaporization^ or of the heating 
surf ace a locomotive engine ought to havCj in order 
to acquire a given velocity, producing at the same 
time its m^ojdmum of useful effect. 

The four questions which have occupied us thus 
far, have had in view to determine one or other 
of the dimensions of the engine, from equation 
(1 his), that is, from the condition that the engine 
draw any given load whatever, at a given velocity. 
But we are now about to suppose that it is required 
to determine the dimensions of the engine, not from 
its effects with any given load, but from the con- 
dition that it produce its maximum useful effect, 
either at a given velocity, or with a given load; 
and as the relation between the dimensions of the 
engine and its maxima effects is expressed by the 
two equations (4 bis) and (5) , namely : 

,^_i s^ D I 

to these we must have recourse in order to attain 
the solution sought. 

Suppose, then, it be required to determine the 
vaporization S, or, in other words, the heating 
surface of the engine, according to the conditiqn 
that it produce its maximum of useful effect at a 
certain given velocity v\ 



OF THE PROPORTIONS OF THE ENGINES. 405 

It is clear, then, that the value of S must be 
derived from equation (4 bis), which will give 

S=5280^-f . ^'9v' (-+P) (H) 

This equation wiU make known the effective vapor- 
ization sought, as soon as v and the dimensions 
of the engine shall be replaced by their values 
supposed fixed or chosen beforehand; and from 
it will be concluded, as in Sect. i. of this chapter, 
the total consumption of water in the boiler, and 
consequently the heating surface necessary to obtain 
the desired effect. 

It will be remarked that, as equation (5) furnishes 
no relation between the vaporization S and the 
maximum load of the engine, the vaporization can- 
not be determined directly, from the condition of 
the engine drawing a certain given load, producing 
at the same time its maximum useful effect. It is 
evident, indeed, that as this condition depends 
entirely on the effort the engine is capable of ex- 
erting, and is altogether independent of the velocity 
of the motion, the question is to be solved only by 
seeking the pressure of the steam in the boiler, 
capable of producing the determined effort; and 
consequently it is in the next problem that its solu- 
tion will be found. 



41G CHAPTER XIII. 

calculatioii then would have remained entirely the 
same, and the solution would obviously not have 
presented more difficulty. 

As a second example, we will suppose it be re- 
quired to construct an engine, csqp^le of drawing, 
1st, a certain given load M. at a desired velocity v., 
on a plane of known inclination, the gravity on which 
shall be expressed by ^, ; and 2ndly, another given 
load M, at a velocity Ukewise known r,, on another 
inclined plane whereon the gravity shall have the 
value g^. 

Here it is plain that the equation (1 bis) or (7), 
which refers to the effects of the engine with inde- 
finite load or velocity, will subsist if we introduce 
into it successively M|, v,, and g^^ M^, t;, and g^^ in 
place of the general values M, v and g. Conse- 
quently there will result, for the solution of the 
problem, the two conditional equations 

« 

By means then of these two equations, any two of 
the dimensions of the engine may be determined, 
and the other three assumed arbitrarily. We may, 
for instance, previously choose, fix>m other con- 
siderations, the pressure in the boiler, the diameter 
of the cylinder, and the length of stroke of the pis- 
ton, and determine the diameter of the wheel and 
the vaporization fix>m the two conditions imposed. 



OF THE PROPORTIONS OF THB ENGINES. 417 

Then, introducing into the above equations, for the 
given loads and velocities and the dimensions chosen, 
their numerical values, those equations will contain 
but two unknowB quantities, which will easily be 
deduced from them by elimination. 

Thus this problem would be as easy as the pre- 
ceding one, and it would be the same with any other 
combination of conditions that might be imposed to 
determine the proportions of the engine. For this 
reason we shall dwell no longer on these researches. 



Sect. X. Of the special influence of each of the 
dimensions of the engine on the effects produced. 

It remains, in fine, as a general conclusion of the 
preceding researches, to specify the peculiar in- 
fluence of each of the dimensions of the engine on 
the effects which are to be expected from it. This 
inquiry will serve to establish fixed notions as to 
the dimensions most favourable for the producing of 
the divers effects that may be required of engines 
about to be constructed. 

1st. Examining equation (1 bis), namely, 

1 2 jL ? 

it will easily be recognised that the velocity of the 
engine with a given load M, will be by so much the 
greater, all things else being equal, as the vaporiza- 
tion S is greater. Moreover, it will also be recog- 

2e 



418 CHAFTBB XIII. 

nified that, for a given vaporization, the velodty will 
be by so much the greater as the fector 

D 

has less value. It is in consequence to be con- 
cluded that, in order to augment to the utmost 
the velocity of an engine with a given load, we 
must either employ a cylinder of the smallest 
possible diameter, or make the wheel the largest 
possible with reference to the stroke of the piston. 

These consequences might however have been 
seen d priori; for if we suppose a given vaporization 
in the boiler, it is dear that the quantity of steam 
which will result fix^m it per minute cannot issue 
forth in the same time, by a cylinder of less 
diameter, except on the condition of increasing 
its velocity during its efflux, that is, of increasing 
the velocity of the piston. As to the ratio between 
the length of the stroke of the piston and the 
diameter of the wheel of the engine, as it is known 
that at every double stroke of the piston the engine 
advances one turn of the wheel, it is readUy per- 
ceived that the larger the wheel relatively to the 
stroke of the piston, the greater must be the ve- 
locity of the engine with a given load. This latter 
circumstance shows also that in order to increase 
the velocity of an engine, it is not absolutely neces- 
sary to augment the diameter of the wheel ; for the 
same end will be attained by diminishing the stroke 



OF THE PROPORTIONS OF THB ENGINES. 419 

of the piston. Thus, on railways of small width of 
way, and on which in consequence it would not be 
advisable to introduce wheels of too great a dia- 
meter, a considerable velocity may be attained by 
proportionally diminishing the stroke of the piston ; 
but this disposition has the inconvenience of ren- 
dering the velocity of the piston much greater for 
the same velocity of the engine. For this reason, 
when more velocity is desired, the better way is 
' always to increase the vaporization ; which beyond 
certain limits requires more width of way. 

2nd. Referring to equation (2), which gives the 
load the engine is capable of drawing at a desired 
velocity, namely : 

(l+»)(*±^) 15280 /+c > dU / J *±/ 

and making, in order to simpliiy, 9 = 0, that is, 
supposing the train to be drawn upon a level, it 
will be recognised that the load is by so much the 
greater as the vaporization S of the engine, that is 
the heating surface of the boiler, is greater; and 
that, on the contrary, it is diminished by the values 
of dy I and D, that is, by the dimensions of the 
cylinder, the stroke of the piston, and the wheel, 
which are proper to augment the velocity of the 
engine. 

Thus an increase of the heating surface of the 
boiler tends to augment both the velocity and the 
load of the engines, but a change in the diameter 
of the cylinder, the length of the stroke and the 



420 CHAPTER XIII. 

diameter of the wheel, is favourable to the velocity 
only at the expense of the load ; and if it be desired 
that the engine should draw a considerable load at a 
given velocity, it must have a large cylinder, a long 
stroke of the piston, and a wheel of small diameter. 
This circumstance explains itself easily, on consider- 
ing first that the greater the diameter of the cylinder, 
the greater is the effort exerted by a given pressure 
of the steam. , As to the influence of the proportion 
of the stroke of the piston to the diameter of the 
wheel, it evidently results from this, that the power 
of the steam acts at the extremity of the radius of 
the crank of the axle, which is equal to the half 
stroke of the piston, whereas the resistance of the 
load acts at the extremity of the radius of the 
wheel ; and it is well known that a force is by so 
much the greater as it acts on a greater lever; 
whence results that the longer the stroke of the 
piston with reference to the wheel, the more ad- 
vantage has the power over the resistance. 

3rd. Examining the value of the useful effect 
produced by the engine at a given velocity, namely, 
from equation (3) : 

and supposing, in order to simplify, ^r = 0, we find 
that this useful effect is augmented, precisely by the 
same causes as the load of the engine ; so that it 
increases with the vaporization of the boiler, but on 



i 



OF THE PROPORTIONS OF THE ENGINES. 421 

the contrary is diminished by the dimensions of the 
cylinder, the stroke of the piston, and the wheel, 
which tend to increase the velocity of the motion. 

The divers e'xpressions of the useful effect neces- 
sarily offer analogous variations, that is to say, the 
dimensions which tend to augment the load will 
have also the result of augmenting the effect of the 
engine, in horse-power, the useful effect produced 
per pound of fiiel and per cubic foot of water va- 
porized, and they will diminish the quantity of coke 
and water necessary to produce the effect of one 
horse, or to draw a ton one mile. 

4th. If we now seek what influence the propor- 
tions of the engine will have on its divers effects, 
the engine producing at the same time its maximum 
useful effect, we first find that, since the velocity of 
maximum useful effect is expressed by the equation 
(4 bis), or 

1 S D 1 

V = 



5280 d^ l + c n+qV 

it is clear that this velocity will be augmented by 
the vaporization of the boiler, as well as by those 
values of d, I and D, which produce a similar effect 
on the general velocity of the engine. Moreover, 
it is reco^sed also that the greater the pressure in 
the boiler, the less will be the velocity of the maxi- 
mum useful effect of the engine ; which arises from 
the circumstance that the steam is less in volume as 
its pressure is greater. 



422 CHAPTER XIII. 



5th. Equation (5) , which gives the TnaTimn m load 
of the engine, 

"- (lV(V±,)D <--'-^'''' - IS? (ra*-"*'")- 

shows that the maYimnin load of the engine is 
totally independent of the vaporization in the 
boiler, and that for given dimensions of the engine, 
it increases precisely when the pressure P of the 
steam in the boiler increases; and this effect is 
owing to the atmospheric pressure then neutraliang 
a firaction by so much the less of the effort applied 
by the engine. As for the rest, the maYimimi load 
is likewise, as in the general case, duninished by the 
dimensions of the engine, which tend to increase 
the velocity. 

6th. Referring to the general conclusions deduced 
from the examination of equation (3), which were 
these, that all the dimensions proper to diminish 
the velocity of the engine, have also the result of 
augmenting its useful effect, it will be recognised 
that, since the case of maximum useful effect is but 
a particular case ot the general one, it must neces- 
sarily be subject to the general conditions already 
expressed. Consequently the maximum useful 
effect of the engines will be augmented by the 
same causes whidi increase the maximum load, 
that is to say, by the increase of the pressure in 
the boiler, by that of the diameter of the cylinder 
or of the length of the stroke of the piston, and 



OF THB PROPORTIONS OF THE ENGINES. 423 

in fine, by the diminution of the diameter of the 
wheel. 

7th. Lastly, on examining equation (7), which 
gives the vaporization of the engine, necessary to 
draw a given load at a desired velocity, namely : 

it is recognised that the vaporization increases with 
the factor 

that is to say, it is so much the greater as the 
diameter of the cylinder and the length of the 
stroke are greater, and that it is on the contrary 
diminished by an increased diameter of the wheels 
of the engine. 



Sect. XI. Of the comparative effects of locomotive 
engines upon the toide-gauge and narrow-gauge 
railways. 

We have just seen in the preceding paragraphs, 
that the only means of really increasing the effects 
of the engines consists in augmenting their vapor- 
ization, that is, the heating surface of their boiler, 
because this mode produces an increase of velocity 
without prejudice to the load of which the engines 
are capable. On the other hand, it is easy to con- 
ceive tiiat on a railway of given width, the dimen- 



424 CHAPTER XIII. 

sions of the engines cannot be augmented inde- 
finitely. It is necessary then to examine here how 
the width of way may limit the size of the boilers, 
and consequently the power of locomotives. 

Almost all the railways of great traffic have been 
hitherto laid down of the width of 4 feet 8^ inches, 
which dimension was founded merely on custom. 
In 1836, when the Great Western Railway was 
made to form the communication between London 
and Bristol, Mr. Brunei, jun., made the road 7 feet 
in width. The question is now to examine what 
advantages may result, with regard to the velocity 
and the useful efiects of the engine, from this widen- 
ing of the road. 

It has been seen above that the locomotives em- 
ployed on the Liverpool and Manchester Railway 
vaporize on an avera^ 65 cubic feet of water per 
hour, and this railway is 4 feet 8^ inches wide. 
On the London and Birmingham, which is of the 
same width, there are locomotives which vaporize 
as much as 100 cubic feet of water per hour, and it 
would be difficult to establish engines having a 
greater vaporizing power on railways of this dimen- 
sion, because the width pf the way would very 
hardly admit of a farther augmentation of the 
dimensions of the boiler. On railways then of 
this width, locomotives of 65 cubic feet of vapor- 
ization may be considered as engines of medium 
force, and engines of 100 feet of vaporization, as 
nearly the most powerful that it is possible to have. 



OP THE PROPORTIONS OF THE ENGINES. 425 

On the Great Western Railway, which is 7 feet in 
width, the engines of medium force vaporize 'about 
120 cubic feet of water per hour, and the most 
powerful in use vaporize as much as 200 cubic 
feet; but considering the interval which remains 
between the boiler and the fieme-work of the 
engine, there is room to think that, on this line, 
engines might be established of 300 cubic feet of 
vaporization, and even more, without very consider- 
ably augmenting the weight of the engine. 

K then, by means of the formulae developed in 
the preceding chapter, we seek the velocity and 
effects which these different species of engines are 
capable of producing, we shall form the Table that 
will be presented a little further on. 

To perform this calculation, we proceed as was 
done in Article III. of the preceding chapter, in 
which the examples reported offer precisely the 
results proper to the engines of medium force em- 
ployed on the two widths of way under considera- 
tion. Thus we adopt the dimensions of the engines 
and the pressure of the steam admitted on each rail- 
way ; we take the presumed friction of the engines at 
15tts. per ton of their weight, as we have deduced 
it from our own researches in Chapter VIII. Simi- 
larly, from what experience "has proved, we take 
the consumption of fuel per cubic foot of water 
vaporized, at 9*2 fts. for engines of 65 cubic feet 
of vaporization, at Sflbs. for those of 100 cubic 
feet, and in fine, at 8"8Ibs. for engines of 120 cubic 



426 CHAPTER XIII. 

feet, 200 cubic feet and above, tbou^ it would 
appeat tbat the consumption of these latter engines 
ought to be less, because the size of the boiler is 
always &yourable to the saving of fiid. To take 
account of the variation of viq[X)rization mth the 
velocity, we likewise adopt, according to experi- 
ment, the vaporizations above indicated as those 
which refer to the respective velocities of 20, 30, 
25, and 35 miles per hour, for the different en- 
gines, taking them in the order in which we have 
placed them. We value the sur£BU» of the carriages 
according to what has been indicated in the two 
examples of Article HI. of the preceding chapter ; 
and finally, we n^ect, for all the engines, the loss 
of steam which may take place by the safety-valves, 
because we suppose tfais loss corrected in all, or at 
least in proportion to the total vaporization, and 
that the divers effects produced will therefore, by 
that cause, be all reduced in a proportional d^ree. 

To establish the comparison of the different en- 
gines on the most usual load, for the convey- 
ance of passengers, we shall seek the velocity and 
the consumption of coke of each engine with a train 
of 50 tons gross, tender not included; and in the 
last column we shall add the maximum velocity that 
the engine is capable of acquiring, drawing its tender 
alone and without any other load. 



OF THB PROPORTIONS OF THE ENGINES. 427 






I 



•8» 

r 

I 



45 2 



1 



5» 

1^ 



*&» 






.8 



4f|| 



r"8 






n 



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s « 



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i 5 



CO 

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CO 

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§ 00 



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St Si 



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SO '^ lO 

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3 > > 5? 



428 CHAPTER XIII. 

Such are then the effects which are to be expected 
firom these different kinds of locomotive engines ; 
and the results which we have just signalized for the 
engines of the London and Birmingham, and Great 
Western Railways, will be found sufficiently con- 
firmed by the experiments made in 1838, on those 
two railways, at the request of the Directors of the 
Great Western, when some difficulty arose respecting 
the width of way.* Taking the mean of such of these 
experiments as were made on trains of about 50 tons, 
having regard to the average vaporization effected 
during the trip, and adding an experiment recently 
published by the Directors themselves of the Great 
Western Railway, in which an engine, similar to 
that of No. 11. of the preceding Table, drew a load 
of 43 tons gross, tender not included, at the velocity 
of 38 miles per hour, consuming 95 lb. of coke per 
ton per mile, it will be recognised that the results 
indicated by the calculation, for the locomotives 
Nos. V. and VI., which have never been built, by 
no means exceed the effects which may be expected 
from those engines. As to the possibility of at- 
taining velocities of 50 and 60 miles per hour, with 
locomotives of sufficient vaporizing power, we deem 
it completely proved by an experiment of our own, 
made on the 3rd August, 1839, on the Great 
Western Railway, with Mr. Daniel Gooch, one of 

* Nicholas Wood's Report to the Directors of the Great 
Western Railway. 



OF THE PROPORTIONS OF THE ENGINES. 429 

the Company's engineers. In this experiment, the 
engine Evening Star, built by Mr. Robert Ste- 
phenson of Newcastle, drawing only the tender 
loaded with eight persons, repeatedly attained the 
velocity of 55 '4 miles per hour ; and if the feeding- 
pipes of the boiler had not been too small for that 
velocity, an arrangement which has since been 
altered, there is no doubt that we should easily have 
maintained* that velocity throughout the trip, and 
even have exceeded it ; but as those pipes could 
not supply the expenditure of the boiler, the water 
in the latter lowered rapidly, and having once at- 
tained the velocity mentioned, we were obliged to 
close the regulator and let the ^[igine run, without 
working, to ^ve time for the boiler to fill again. 
The results deduced from our formulae and con- 
tained in the Table presented above, appear then 
to us to be completely supported by the facts. 

Thus it is manifest that locomotive engines on 
wide-gauge railways can draw the * same average 
load of 50 tons, or about 200 passengers, at much 
greater velocities than the engines on narrow-gauge 
railways, and that the velocity of the former may 
even amount to double the velocity of the latter. 
Such an advantage is certainly not to be neglected, 
and it would be vain to object that the present 
velocity is sufficient ; for that argument might have 
been urged, either some years ago against the esta- 
blishment of mail-coaches, or in our days against 
any establishment of railways whatever. 



J 



430 CHAPTER xin. 

It will be remarked, in the pre<iedii]g results, that 
the surfdos velocity is purchased by a greater ex- 
pense of fuel. This surplus of expense arises 
undoubtedly in part from the excessive wei^t of 
the engine and its tender, which together amount 
to about 30 tons, instead of 15, which is the cor- 
responding weight for engines on narrow-gauge 
railways ; so that, for a load of 50 tons, the motive 
power is affected with a weight of 30 tons in the one 
case, and with a weight of but 15 tons in the other. 
But that effect depends also especially on the 
circumstance, that the resistance of the air, the 
pressure in the blast-pipe, and the other passive 
resistances, consume quantities of work by so much 
the greater as the motion is performed with greater 
velocity. It is then an inevitable result of the 
velocity, whatever may be the width of way, and the 
engine employed. To obtain conviction moreover 
that the inconvenience of the greater weight of the 
mover may be counterbalanced by opposite ad- 
vantages, it suffices to compare the two species 
of engines at the same velocity. Now, calculating 
the load that a wide-gauge locomotive engine of 
medium force, or of 120 cubic feet of vaporization, 
can draw at a velocity of about 25 miles per hour, 
we find, as may be seen in the example calculated 
in Article III. of the preceding chapter, that that 
load will be 147 tons, tender included, or 137 
tons without the tender, and that the corresponding 
consumption of fuel will be '30 ft. of coke per 



OF THE PROPORTIONS OF THE ENGINES. 431 

ton per mile. Comparing then this effect to that 
of an engine of medium force of the narrow-gauge, 
or of 65 cubic feet of vaporization, we have the 
following results : 

Velocity, in Load, in Coks» in 

mQa per tans gnm, Itm* per 

boaif tender not ton per 

indnded. mile. 

Engine of 65 cable feet of 

vaporization, narrow-gauge .. 25*10 50 '47 

Engine of 120 cubic feet of 

vaporization* wide-gauge .... 25*55 137 *d0 

Consequently, when a velocity of 25 miles per 
hour is considered sufficient, it is ohvious that wide- 
gauge locomotive engines have the advantage of 
conveying much greater loads, and consuming less 
fuel per ton. 

We are then of opinion, that in countries where 
as yet but few railways are made, it is worth con- 
sidering whether, according to the circumstances, it 
will not be advantageous to employ a greater width 
of way than that in general use, and we must here 
add that, for the most powerful engines of the above 
Table, a way 6^ English feet in width appears to be 
sufficient. 



Sect. XII. Practical formuUB, to determine the 
proportions of locomotive engines^ according to 
given conditions. 

Before terminating this chapter, we will here 
give, in their numerical form, all the formulae which 
we have just presented, to determine the proper- 



432 CHAPTER XIII. 

tioDS of the engines, according to given conditions. 
For the signification of the signs employed, we refer 
to Article III. Chapter XII.; and for the use and 
complete intelligence of the formulae, we refer to 
each of the respective sections of the present 
chapter. 

PRACTICAL FOEMOUB TO DETBRMINB THE FEOPOETION8 OF LOCO- 
MOTIVE ENGINES, NECBSSAET TO FEODUCE GIVEN EFFECTS. 

Total vaporizstion 

of the boiler, in cii> 
bic feet of water 
per hoar. 

w •••'''=?• 27^'7Cni- 1 - («±')*'^'~-~'- if J •• • 

Square of the dia- 
meter of the cy- 
linder, in feet. 

stroke of the piston, 

in feet. 

no) D-i!i iizi+p't, 

Y7j--(6±y)M+^-«e«-_ 

IHameter of the 

wheel, in feet. 

(ll)...S- yij.^'.tr'(618 + P) Total vaporization 

of the boiler, in cu- 

« 

bic feet of water 
per hour. 

(12)...P = (l + 8)J^[(6±^)M±^+w'2+ -L_] +2118+/>'r' 

Total or absolute 

pressure of the steam 
in the boiler, in 
pounds per square 
foot. 



• « • 



OF THE PROPORTIONS OF THE ENGINES. 433 

(13)...P*784^-.i-618 Total or absolute 

pressure of the steam 
in the boiler, in 
pounds per square 
foot. 

(I4),..rf««784~. i._i-_ Square of the dia- 

/ V 618 + P . ^ XV 

meter of the cy- 
linder, in feet. 

(15).../=. 784^.?;.-~J — Stroke of the piston, 

«' V 618 + P . ^ J. 

m feet. 

(16)...D«-L.rfa/.| (6i8^.p) Diameter of the 

wheel, in feet. 

(17) . . . rf8« (1 + a) -.^ ,— ii? .. Square of the dia- 

^' P-21l8~^'r' ^^, ^ the cy. 

Under, in feet. 

i6±g)W±ffm + uv'' + -^ 

{18)..../=(U-8)£.. p ouB „V • S*«>1^«°^*«^ ?«*«"' 

d^ P- 2118-^ 17 inieeL 



/iftv r. ^f P-2118-/?'r' _. ^ . . 

(19) . . . D== - — . s- • • • • Diameter of the 



(6 +^)M'+mii + !•»'>+ ; — - wheel, in feet. 

~ — 1 + 



2f 



CHAPTER XIV. 



OF ADHESION. 



In the two preceding chapters, we have given the 
formulae for calculating the effects or the proportions 
of the engines ; but we must now speak of another 
condition without which the effects indicated could 
not be produced. This condition consists in the 
adhesion of the wheels to the rails being sufficient to 
effect the motion of the load. 

It has been observed, in the description of the 
engine, that the effort of the steam being applied to 
the wheel, the engine is precisely in the casef of a 
carriage which is made to advance by pushing at the 
spokes. Thus, as in this action the only fulcrum of 
the mover is the adhesion of the whed to the rails, 
if that adhesion were insufficient, the force of the 
steam would indeed make the wheels turn; but 
these, sliding on the rails instead of adhering to 
them, would turn without advancing, and the 
engine would remain on the same spot. 

The heavier the train to be drawn, the more force 
the engine must employ, and the more resistance 
it must consequently meet with at the point on 
which it strains to effect the motion. It might then 



OF ADHESION. 435 

be feared that with trains of considerable weight, the 
engines would be unable to advance ; not that force 
would be' wanting in the mover itself, but in the 
fulcrum of the mover. 

The experiments presented in Chapter XII. esta- 
blish the measure of that adhesion in the fine 
weather season. In all these experiments, not one 
is found in which the motion was stopped or even 
slackened for want of adhesion. And yet we find 
among them loads amounting to above 300 tons. 

If, for instance, we refer to the first experiment 
made with the Fury on the 24th July, and take 
account of the gravity in ascending the plane in- 
clined ^, we shall find that the engine then drew a 
load equivalent to 306 tons on a level. Since the 
engine advanced with this load, it foUows that the 
adhesion was sufficient. Now the weight of the 
Fury is 8*20 tons, and that weight is so divided 
that 5'5 tons bear on the hind-wheels, which are 
the only propelling ones, the fore-wheels not serving 
at all to urge the engine forward, but merely to 
support it. It was then a weight of 5*5 tons that 
drew 306 tons, or a weight 55 times as con- 
siderable as itself; consequently, an engine having 
its four wheels coupled, and thus adhering by its 
whole weight, may draw a load equal to 55 times its 
own mass. 

We have said that the engine Fury adheres but 
by two wheels. This disposition is general on the 
Liverpool Railway for all the trip engines, because 



436 CHAPTER XIV. 

the adhesion of two wheels is sufficient for the 
loads they have to draw. As to the engines which 
serve as assistant engines on the inclined planes, 
they work with the adhesion of their four or six 
wheels, as has been said elsewhere. The engine 
Atlas is the only one employed for the trips, which 
differs from the others in this respect. This engine 
has six wheels, four of which, of equal size, are set in 
motion by the piston. The other two, smaller and 
without flange, may be raised out of contact with 
the rails by the action of the steam on a moveable 
piston. This disposition, which prevents these 
latter wheels from being inconvenient in turning, is 
due to Mr. John Melling, sen., of Liverpool. 

To Mr. Melling also is due another very ingenious 
arrangement, by means of which an engine may be 
made to adhere by all its wheels, notwithstanding 
the difierence of their diameters. It consists of a 
pulley, which is let down at pleasure between the 
two pairs of contiguous wheels, and which connects 
them so that one cannot turn without necessarily 
drawing the other with it. By means of this ap- 
paratus, engines may have their- wheels \inequal, 
which is very advantageous to the good arrangement 
of the machinery, and all their wheels need be put 
in communication only at the moment when that 
becomes necessary, which is done without stopping 
the engine. 

We have just expressed the adhesion, by giving 
the measure of its effects ; *but that force itself may 



I 



OF ADHESION. 437 

be expressed in a direct manner. The load of 306 
tons produced a resistance, or required a tiPaction of 
1836 lbs. ; the adhesion was then equal to at least 
1836 lbs., otherwise the w^heel would have turned 
without going forward. Now the adhering weight 
was 5'5 tons, or, expressed in fts., was 12,320 lbs..; 
it is plain then that the adhesive force was equal to 
about ^ of the adhering weight. Considering that 
every 6 lbs. of force corresponds to the traction of 
1 ton on a level, this expression amounts to the 
same as the first. 

In winter, when the rails are greasy and dirty by 
the effect of wet weather, the adhesion diminishes 
considerably. However, unless in very extraor- 
dinary circumstances, the engines are always ca- 
pable of drawing a load of 15 waggons or 75 tons, 
tender included, that is, 14 times their adhering 
weight ; or, in other words, as the resistance of 75 
tons is 450 lbs., the adhesive force is always at least 
^ of the adhering weight. 

Adhesion being indispensable to the creation of 
the progressive motion, two conditions are requisite 
for an engine to be capable of drawing a given load : 
1st, the dimensions and proportions of the engine 
and its boiler must enable it to produce, by means 
of the steam, the necessary pressure on the piston, 
which constitutes the force applied by the engine ; 
and 2nd, the weight of the engine must be such as 
to cause a sufficient adhesion to the rails. These 
two conditions of force and weight should accord 



438 CHAPTER XIV. 

together ; for, were there a great force ci steam and 
a slight SdhesioD, the latter would limit the effect of 
the engine, and steam would be lost; and were 
there too much adhesive weight for the powor of 
the engine, that wei^t would, during the motion, 

m 

become a useless burdoi, since the limit of the load 
would then be marked by the pressure of the 
steam. 

It is necessary therrfore, after having determined 
the dimensions of the engines from the conditions 
which they are to fulfil, as has been done in the 
preceding chapter, to seek what ou^t to be their 
weight so as to enable them to draw the greatest load 
intended to be imposed on them during thdr work. 
The enormous weight now given to locomotive 
engines, generallj^ causes this condition to be ful* 
filled of itself. Six- wheel engines however require, 
in this respect, more attention than four-wheel 
engines, because it often happens, on an uneven 
railway, that a six-wheel engine is wholly suppcurted 
on its four extreme wheels, whereas the middle 
ones, which are the propelling wheels, being acci- 
dentally situated immediately above a low part of 
the railway, scarcely touch the rail, and therefore 
have but a slight adhesion. 



CHAPTER XV. 



OF THE REGULATOR. 



Sbct. I. Of the effects of the regulator on the 

velocity of the engine. 

It has been said, in the description of the different 
parts of the engine, that the pipe which brings the 
steam from the boiler to the cyUnders may be 
closed, either entirely, or in part, by means of a 
cock or regulator, and that the velocity of the 
engine is regulated by this means. U becomes 
necessary then to consider how this effect is pro- 
duced, and how the formulae which we have given 
may keep accoimt of it. 

It is an opinion generally received, that by 
opening or shutting the regulator more or less, the 
pressure of the steam in the cylinder is augmented 
or diminished. But we have proved that the pres- 
sure in the cylinder is always strictly determined, 
a priori, by the resistance of the load against the 
piston. So long therefore as the load shall not 
vary, the pressure in the cylinder will not vary, and 
consequently the greater or less opening of the 
regulator can make no difference in it. Besides, 



440 CHAPTER XV. 

how could the contraction of a passage change the 
pressure of a gas or steam issuing through that 
passage ? It may indeed change its quantity, be- 
cause the smalhiess of the aperture prevents more 
than a certain volume from passing in a given time ; 
but unquestionably it can never change the pressure, 
for it will always happen that as soon as the steam » 
having got through the passage, shall arrive in the 
cyUnder, and shall there acquire the pressure of the 
resistance, the piston will recede without allowing it 
to assume a higher pressure. And if it be supposed 
that by enlarging the passage, the steam may be 
made ta come ten or twenty times quicker, the 
piston will recede ten times or twenty times quicker 
also, since its motion is the result of the arrival of 
the steam; but the pressure in the cylinder can 
never exceed the resistance of the piston, because 
the piston being nothing more nor less than a valve 
to the cylinder, it would be supposing a boiler in 
which the pressure of the steam should be greater 
than that of the safety-valve. 

Thus the narrowing of the regulator cannot 
diminish the pressure of the steam in the cylinder. 
Moreover, a diminution of pressure in the cylinder 
would not account for the diminution of velocity of 
the engine, which is observed when the regulator 
is partially closed ; except indeed the motion should 
be attributed, as it has been by some, to an excess 
of the pressure of the steam in the cylinder above 
the resistance of the piston. But this opinion 



OF THK RBGULATOR. 441 

would be altogether an error; for if such excess 
existed, the motion of the engine would not be 
uniform, but indefinitely accelerated. On the con- 
trary, the pressure of the steam is equal to the 
resistance of the piston, and the motion is owing to 
the velocity with which the steam arrives, at that 
pressure. Hence, the above-mentioned suppositions 
are inadmissible. But the effects of the regulator 
are easily accounted for in another manner. 

The quantity of steam of a given density, which 
issues forth through a determined orifice, being in 
the ratio of the area of that orifice, it follows that if 
we lessen the orifice of the regulator, we shall 
thereby diminish the quantity of steam, at the 
pressure of the boiler, which can issue by the orifice 
of the regulator to pass into the cylinders. If how- 
ever the fire be kept up at the same degree of 
intensity, it will continue to produce the same 
quantity of steam per minute. This steam, which 
can no longer flow in totality towards the cylinder, 
will therefore accumulate in the boiler, and there 
rise to a still greater and greater density and elastic 
force, till at last it be able to find some outlet. 

Now the steam has two outlets whereby to escape 
from the boiler, namely : the passage of the regu- 
lator, which, notwithstanding its contraction, would 
admit 4:^ the total efflux of the steam, as it is gene- 
rated, if that steam acquired a sufficient degree of 
density, or, in other words, a volume sufficiently 
small for that efiect ; and the safety-valve, which 



442 CHAPTER XV. 

would equally admit of its escape, were the steam 
to acquire a pressure sufficient to raise the valve. 
Two cases then will occur, according as the steam, 
continuing to accumulate in the hoiler, shall acquire 
more promptly either the pressure which admits of 
its issue by the safety-valve, or the density which 
enables it to flow out entirely by. the regulator. 

1st. If the r^ulator is much contracted, and if 
the safety-valve of the boiler, on the contrary, is 
fixed at a moderate pressure, the steam retained in 
the boiler will soon attain the d^ree necessary to 
raise the safety-valve. The valve then will be open, 
and all the surplus steam generated in the boiler, 
beyond what can issue by the regulator, will escape 
into the atmosphere ; and this effect will continue 
so long as nothing shall be changed in the engine, 
because there will still be the same necessity for 
the steam to effect its efflux as it is generated, and 
because the resistance of the obstacles which it has 
to overcome will remain still the same. 

Thus, the effect of the contraction of the regulator 
will be, to cause a portion more or less of the steam 
produced by the boiler to be lost in the atmosphere ; 
and as the effects of the engine are attributable only 
to the effective vaporization, that is to say, to the 
portion of the total steam which really penetrates 
into the cylinders, it follows that the velocity of the 
engine will be reduced precisely in proportion to 
the quantity of steam lost. Hence, the effect of 
the contraction of the regulator will be to reduce 



OF THE REGULATOR. 443 



\ 



the velocity of the engine immediately. Then, after 
the first few moments of the contraction of the re- 
gulator, the. engineer seeing a considerable quantity 
of steam running to waste by the safety-valve, will 
naturally cease to keep up his fire with the same 
activity. The vaporization produced in the boiler 
will be diminished in consequence; and by con- 
tinual reduction of the fire there will at last be no 
more steam generated than may efiectively pene- 
trate into the cylinders. From this moment then 
the blowing of the safety-valve will cease, and the 
velocity of the engine will continue as it was regu- 
lated at first by the contraction of the regulator. 

Consequently it is manifest that the regulator 
diminishes the velocity of the engine, by imme- 
diately reducing the effective vaporization, and ul- 
teriorly the total vaporization of the boiler ; and it 
is also manifest that its effect is not to diminish the 
pressure in the cylinder, but to augment the pres- 
sure in the boiler. 

2nd. We have just supposed the case wherein the 
regulator is sufficiently contracted to make the 
safety-valve blow, and have seen what effects will 
result therefrom. But another case may occur, 
namely : that in which the regulator should also be 
contracted, but yet not sufficiently so to make the 
safety-valve blow ; that is to say, the case wherein 
the steam, accumulating in the boiler, should attain 
the density which permits its total efflux by the 
regulator, before it attains the pressure necessary 
to raise the safety-valve. Then, since the valve 



444 CHAPTBB XV. 

does not blow, and no portion of the steam pro- 
duced is lost, it is clear that all the steam will pass 
into the cylinder and act there as before. Hence the 
velocity of the engine will in nowise be changed ; 
for that velocity cannot be augmented nor dimin- 
ished except by an increase or a reduction of the 
effective vaporization of the engine, and this cir- 
cumstance does not occur in the case supposed.- 

Notwithstanding, therefore, the contraction of the 
regulator, the velocity of the engine will remain the 
same, and there will result, as in the preceding case, 
only an increase of pressure in the boiler. 

From these considerations, we see that the unique 
and immediate effect of the contraction of the regu- 
lator is to augment the pressure of the steam in the 
boiler ; and that if the increase of pressure is such 
as to cause a loss of steam by the safety-valve, the 
velocity of the engine will be reduced precisely in 
the same proportion, but that if no such loss takes 
place, the velocity undergoes no reduction. 

Now, in the formulae which we have given to 
calculate the velocity of the engines, the quantity S 
represents the effective vaporization of the engine, 
that is to say, the quantity of water which, being 
converted to steam, really penetrates into the cylin- 
ders and acts upon the piston. If, notwithstanding 
the contraction of the regulator, there is no loss of 
steam by the safety-valve, the effective vaporization 
of the engine will not be changed, that is, the 
quantity S will remain the same, and consequently 
the formulae will still continue to give the same 



OF THE REGULATOR. 445 

result for the velocity of the engine. On the other 
hand, if a loss of steam takes place by the safety- 
valve, that loss must obviously be subtracted from 
the total vaporization of the boiler, in order to 
deduce from it the effective vaporization, or the 
quantity which ought to be substituted for S in the 
equations, and then the result of those formulae will 
be reduced in a proportionate quantity. In either 
case, therefore, the formulae which we have given 
will always continue to make known the true effects 
produced by the engine. All they require is, that 
account be taken of the loss by the valves, when 
that loss occurs, and we have already shown in 
Chapter X. how it may be estimated. 

These considerations will be found confirmed by 
the experiments presented in Chapter XII. It will 
there be observed that the formulae give results 
quite as exact for the case wherein the regulator was 
partially closed, as for the case in which it was 
entirely open. And the reason is this, that when 
the partial close of the regulator was attended with 
a loss by the- valve, we took account of it in the 
value of the effective vaporization S, by taking that 
value equal to the total vaporization of the engine, 
diminished by the. loss at the valves. 

Sect. II. Dimensions of the steam-passages in some 

locomotive engines. 

We will close this chapter by giving the diameter 
of the steam-pipes in the engines which we sub- 
mitted to experiment, and in some others whose 



446 



CHAPTER XV. 



dimensions have been given at the beginning of this 
work. The pipes here considered are those which 
lead separately from the boiler to each slide-box. 
Those which afterwards lead from that box to the 
cylinders, are of a corresponding surface, though of a 
different shape. For instance, when they form the 
continuation of a tube 3 inches in diameter, they are 
made 7 inches long by 1 inch wide, which presents 
the same surface for the passage of the steam. 

It will be remarked that the steam-passages are 
much wider in locomotive engines than in stationary 
steam engines, since in these the area of the steam- 
passage is but ^ of the area of the cylinder, while 
in locomotive engines the proportion between the 
same parts is in general i^ . 



Steam-pipes in some of the locomotive engines of the lAoer- 

pool and Manchester Railway, 



Name of the 


Diame- 
terofthe 


Stroke 
of the 


Heating sur&ce 


Inner dia- 
meter of 
the steam- 


of the 


of the 


engine. 


cylinder. 


piston. 


fire-box. 


tubes. 


pipes. 




inches. 


inches. 


sq. feet. 


sq. feet 


inches. 


Samson. 


14 


16 


40-20 


377-41 


3-25 


Goliath I. 


14 


16 


40-31 


355-84 


3-25 


Atlas. 


12 


16 


5706 


197-26 


3-25 


Vulcan. 


11 


16 


34-45 


267-84 


3-50 


Fury. 


11 


16 


32-87 


267-84 


3-50 


Vbbta. 


IH 


16 


4600 


215-66 


3-25 


Lexdb. 


11 


16 


34-57 


267-84 


3-50 


FiRBFLT I. 


11 


18 


43-91 


317-71 


300 


Star. 


14 


12 


49-71 


279-18 


3-75 



CHAPTER XVI. 

OF THE LEAD OF THE SLIDE. 

Sect. I. Of the nature and effects of the lead of the 

slide. 

Wb have said, in describing the different parte of 
the engine, that it is the^lide which successively 
opens and shute the steam-ports above and below 
the piston, so as to apply the effort of the steam 
alternately on each side. Were the engine regulated 
as it might seem natural to regulate it, the slide 
would keep the steam-port open till the piston 
arrived at the bottom of the cylinder. At this 
moment it would change: the first passage would 
be closed, and the opposite one opened. Then the 
motion of the slide would exactly accompany that of 
the piston, that is to say, their alternations would be 
strictly simultaneous. 

But the thing is not so ordered. At the moment 
when the piston is about to terminate ite stroke, it 
is needless and even detrimental to the engine to 
apply any new impulsion on it, since it is then* at 
the moment of stopping, to perform ite retrograde 
stroke. Besides, it is proper to allow the steam, 



448 CHAPTBR XVI. 

which now fills the cylinder, time to escape as much 
as possible, before the piston is brought back in a 
contrary direction, since it would otherwise con- 
tribute to form an obstacle, on account of the small- 
ness of the orifice of the blast-pipe ; and finally, 
rather than let the piston strike against the end of 
the cylinder, or exert at least an effort in that 
direction against the crank of the axle, it is prefer- 
able to present to it an elastic body which may 
deaden its shock. With this threefold purpose, 
then, the motion of the slide is regulated in such 
sort, that successively, and before the piston reaches 
the end of the cylinder^ the three following opera- 
tions are performed: 1st, the communication is 
intercepted between the boiler and the steam-port 
through which the steam is actually coming, which 
suspends all addition to the motive force ; 2dly, the 
communication of the same port with the waste 
steam-port is opened, which permits the escape of 
the steam by anticipation, while it still continues 
its action ; 3rdly, the communication between 
the boiler and the steam-port which conducts the 
steam upon the piston, in a contrary way to its 
motion, is opened ; which deadens the shock of the 
piston, reKeves the joints of the machinery, and 
enables the steam to act with full force on the 
piston, as soon as the latter begins its retrograde 
stroke. These three successive operations, as we 
have said, are performed before the piston reaches 
the bottom of the cylinder, and, by means of divers 



OF THE LEAD OF THE SLIDE. 449 

dispositions, they may be so regulated as to take 
place on points more or less anterior to the end of 
the stroke. 

When the engine is regulated as we have just 
explained, it is visible that at the moment when the 
piston terminates its stroke to begin another, the 
slide has already, for a certain space of time, been 
intercepting the coming of the steam in favour of 
the motion, and has even already admitted it in the 
contrary direction during another interval of time 
less than the former ; or, in other words, the slide 
has already traversed a certain space in the di- 
rection of its stroke, from the moment when it 
closed the first passage, and another space less than 
the former, from the moment when it opened the 
contrary passage. It is this anticipation of the 
motion of the slide upon that of the piston which is 
called the lead of the slide^ because it indicates by 
how much the motion of the slide precedes that of 
the piston; but it is conceivable, from what has 
been said, that a distinction is to be made between 
the lead of the glide for the suppression of the steam, 
and the lead of the slide for the admission of the 
steam, though the latter is more particularly under- 
stood when it is simply said the lead of the slide. 
These two sorts of lead are sometimes distinguished 
by saying the lead on the exhausting side and the 
lead on the boiler side, but the former mode appears 
to us to be more exact. 

When the slide valve is single, that is to say, con- 

2g 



450 CHAPTER XVI. 

sisting of a single box, like that of fig. 26 (PI. IV.) » 
the difference between the two leads is equal to 
twice the overlap of the slide. In effect, on ex- 
amining that figure, which represents the slide at the 
moment when it changes the passages of the steam, 
and supposing its motion to have been in the direc- 
tion of the arrow, it will be recognised that as soon 
as the slide arrives at the position a, the coming of 
the steam is intercepted in the left-hand passage, 
but that the right-hand passage does not begin to 
open till the sUde attains the position c. If then we 
suppose the passage still more opened, and the 
slide arrived at the position d at the same time that 
the piston reaches the bottom of the cylinder, it is 
plain that the quantity cd hy which the passage is 
then open, will be what we call the lead of the slide 
for the admission of the steam ; but that the oppo- 
site passage will have been shut, and consequently 
the motive force, in the direction of the motion, 
will have been intercepted from the point a, that is 
to say, the lead for the suppression of the steam will 
necessarily be equal to the lead of admission aug- 
mented by twice the overlap of the sUde. When 
the sUde is double, or composed of two boxes which 
may be set further apart or nearer to each other at 
pleasure by means of an adjusting ' screw, each lead 
may be regulated separately at the point which may 
be judged suitable, and this is an advantage, but the 
slide is more liable to get out of order. 

As the disposition of the slide; which has just 
been described, has the result of suppressing the 



OF THE LEAD OF THE SLIDE. 451 

motive force, at a certain point of the stroke of the 
piston, to introduce it afterwards in the contrary 
direction, it is evident that its effect on the engine 
cannot be calculated till after an exact determination 
of that point of the cylinder, at which the piston is 
at the moment when the close and the opening of 
the respective passages take place. This is there- 
fore the first inquiry that wiU occupy our attention. 
With this view, we return to the single slide 
valve represented in figs. 10 and 26. On ex- 
amining these two figures, it will be perceived that 
if the radius of the eccentric were strictly at right 
angles with the radius of the crank, it would then 
so happen that the sUde would be in its middle 
position, indicated by the figure, precisely at the 
moment when the piston should arrive at the end 
of its stroke. In this case, the suppression of the 
steam in favour of the motion would take place, be- 
fore this point, by a distance equal to the overlap 
of the slide on the two ports ; and the admission of 
the steam by the opposite passage would take place, 
after that same point, by a distance equal to the 
same overlap. But if it be wished to give the 
engine a certain lead of the slide for the admission 
of the steam, the passage of the steam opposed to 
the present motion of the piston must be already 
open a certain quantity, at the moment when the 
piston terminates its stroke. To this end, therefore, 
the radius of the eccentric must incline forward, 
from the perpendicular to the radius of the crank, 



452 CHAPTER XVf. 

in an angle corresponding to the lead in question 
augmented by the overlap of the slide. In effect, if 
it be thus, we see that when the radius of the crank 
coincides with the horizontal line, that is to say, 
when the piston is at the end of its stroke, the 
radius of the eccentric has passed the vertical by a 
quantity corresponding to the lead of admission plus 
the overlap ; that is to say, the slide has passed its 
middle position, just the quantity necessary to open 
the steam-port the quantity indicated by the lead. 

This premised, suppose 6 D' (fig. 27) to represent 
the radiiDS of the crank, and hb' the radius of the 
eccentric. When the radius of the eccentric co- 
incides with the vertical, the slide is in its middle 
position and all the passages are closed. After it 
has passed this point a quantity equal to the over- 
lap, the passage of the steam opposed to the motion 
of the piston will begin to open, and when the radius 
of the eccentric shall have reached fteT, the slide will 
open that passage the quantity indicated by the 
lead. But since the eccentric and the crank turn 
in one piece with the axle of the engine, it follows 
that their radii describe equal angles in the same 
time. Hence, while the radius of the eccentric 
describes the angle ft'ftcT, the radius of the crank 
describes an angle D'6B equal to. the former. On 
the other hand, while the eccentric describes the 
angle Vhd\ the slide, which moves horizontally, 
traverses the space 6rf, which is equal to d!p ; that 
is to say, it traverses the sine of the angle Vb^^ in 



OF THE LEAD OF THE SLIDE. 453 

a circle whose radius is equal to that of the eccen- 
tric. Similarly, while the crank describes the angle 
D'6B, the piston traverses the space DB, that is, 
the versed sine of the angle described, in a circle 
whose radius is equal to that of the crank. 

Finally therefore, while the slide, departing from 
its middle position, performs the sines of the angles, 
in the circle of the eccentric, the piston, to finish its 
stroke, performs the versed sines of the same angles, 
in the bircle of the crank. Consequently it will 
be easy to find the correlative situations of those 
two pieces. It wiD suffice for this purpose, in prac- 
tice, to draw exactly and by the scale the figure 27, 
in which bs is the radius of the eccentric or the half 
range of the slide, &B the radius of the crank or the 
half stroke of the piston, and db the distance at 
which the sUde is supposed to be from its middle 
position. Then, raising at the point c2, the perpen- 
dicular dcty we have the point df ; afterwards taking 
the angle B6iy equal to the angle b'bd\ we deter- 
mine the point D", and finaUy, letting fall the per- 
pendicular DD, we have definitively the distance 
DB, between the point D, where the piston then is, 
and the point B which is the end of its stroke. 

If it be desired to find the quantity DB by calcu- 
lation, it will suffice, from what has just been said, 
to consider the given distance db as the sine of an 
angle, and to seek the corresponding versed sine. 
Therefore, the ratio of the line db, to the radius bs, 



454 CHAPTER XYI. 

of the circle in which that line is drawn, must be 
found; which is easy, since those two lines are 
known. Then the logarithm of that ratio must be 
taken, and that logarithm sought in the column of 
sines of a Table of ordinary sines. Close to this will 
be found the logarithm of the corresponding cosine, 
and consequently on seeking the number which that 
logarithm represents, the cosine of the angle de- 
scribed will be known. Subtracting this cosine 
firom unity, the difference will be the versed sine of 
ihe same angle. This will then be the ratio between 
the line DB and the radius &B of the circle in which 
that line is drawn. Consequently, as the line &B is 
known, it will be easy to determine from it the ab- 
solute measure of DB the line sought. 

If we take for example an engine in which the 
stroke of the piston is 16 inches, range of the slide 
3 inches, overlap of the slide over the steam-ways 
^ inch ; and if we suppose the engine to have a lead 
of admission of f inch, and a lead of suppression of 
i inch ; and it be required to find at what distance 
from the end of the cylinder the piston is when the 
steam is intercepted, and at what point it is when 
the steam is introduced against it, we shall find by 
following the calculation indicated above, and ap- 
plying it successively to the two given distances, 
that the space remaining for the piston to traverse 
at the moment the steam is intercepted in favour of 
the motion, is 1*50 inch ; and that when the steam 



OF THB LEAD OF THE SLIDE. 455 

is introduced in the opposite direction, the piston is 
'73 inch from the end of its stroke. The figure 27, 
constructed by the scale, gives the same result. 

If we suppose in the same engine a lead of i and 
f inch in each respective direction, we find by a 
similar calculation, that the space remaining for the 
piston to traverse when the arrival of the steam is 
inteircepted in the direction of the motion, is '25 
inch, and that the steam is introduced in the oppo- 
site direction when the piston is '03 inch from the 
end of its stroke. 

These examples show how, when the lead is 
given, or when the situation of the slide is known at 
any moment whatever, the point at which the pis- 
ton is at the same moment may always be deduced 
fr6m it. 



Sect, II. Of the effects of the lead of the slide on 

the velocity of the engine. 

We have already mentioned the advantages arising 
from the lead of the slide, with regard to the play 
and the conservation of the engine ; but there is 
another advantage no less important, resulting from 
this disposition, namely, that of obtaining a greater 
velocity, and consequently a greater useful effect 
of the engine with a given load. 

This effect is easy to comprehend ; for if the sup- 
pression of the steam from the boiler, instead of 
being made precisely at the end of the stroke of the 



456 CHAPTER XVI. 

piston, takes place, for instance, at the moment 
when the piston is yet an inch from the bottom 
of the cylinder, from that moment steam ceases to 
flow into the cylinder. Thus, with r^ard to the 
quantity of steam admitted into the cylinder or 
expended at each stroke of the piston, the length 
of the stroke is really diminished an inch. Now it 
is the quantity of steam produced by -the boiler 
which regulates and limits the velocity of the engine. 
Suppose that such production frumished m cylinders- 
full of steam per minute, when the total length I of 
the stroke was filled with steam : now no more than 
the length I— a is filled with steam; the same produc- 
tion then will fill per minute a number of cylinders 

expressed by wi X Hence, in fine, the velo- 

city of the engine will be increased in the inverse 
ratio of the lengths of the cylinder which are filled 
with steam. 

It is to be observed, indeed, that while a lead is 
given to the slide, to suppress the steam coming 
fix)m the boiler, a lead is also given to admit the 
steam against the piston, before the latter has 
reached the bottom of the cylinder. There results 
then an increase in the mean resistance opposed to 
the motion of the piston during the whole of the 
stroke ; and since the velocity of the engine de- 
creases as the resistance which it has to overcome 
becomes greater, it might be deemed that this cir- 
cumstance compensates for the former. But as, by 



OF THE LEAD OF THE SLIDE. 457 

means of double slide valve boxes, it is possible 
to have a considerable lead for the suppression of 
the steam, and a very small one for the admission of 
the steam in the contrary direction, and as, even 
with single slide valves, the steam is never ad- 
mitted against the piston but when the latter is at 
a very small distance from the end of the stroke, 
and consequently at a point where a great force 
could produce but a very small effort against the 
motion of the crank of the axle, it will be recognised 
that this circumstance will not sensibly retard the 
progress of the engine. It may then be ^generally 
admitted that the velocity of the engine will increase 
in the ratio of the total stroke of the piston, to the 
portion traversed at the moment of the suppression 
of the steam by the effect of the slide. 

This premised, it is visible, from the calculation 
which we have given in the preceding section, that 
when the lead of the slide for the suppression of the 
steam is but f inch, on a total range of 3* inches, 
the increase of the velocity of the engine must be 
inconsiderable, since the steam is then suppressed 
on '25 inch only, or on ^ of the total stroke of the 
piston. If the lead of suppression amount to f or 
f inch, it produces a more sensible effect, which 
nevertheless may easily be compensated by the 
strength of the wind, by care in maintaining the 
fire, or by the quality of the fuel ; but if it amount 
to i inch, calculation shows that it may produce 
an augmentation of about two miles on a velocity 



458 CHAFTSR XVI. 

of thirty mfles per hour ; and in this case as weD 
as in those in which the lead is greater still, it is 
concetvable that its effects must mviifest themselyes 
in practice. 

Among all the engines employed in the experi- 
ments presented in Chapter XII., there was not one, 
except the Vbsta ^vrtiich we shall presently notice, 
in which the lead of the slide was in the case last 
m^itioned, that is, in which the lead of the slide 
could have any very sensible effect on the velocity. 
It is besides to be observed that when, in Chapta 
X., we determined the effectioe -vaporization of the 
engines, or the loss of water carried with the 
steam in a liquid state, we did, in fact, take 
account of the lead of the slide for each engine. 
In effect, since the engine had then a lead of the 
slide, we ought to have calculated the cylinder- 
full, not by the entire stroke of the piston as we did, 
but by the stroke after deducting the portion cor- 
responding to the slide ; that is to say, retaining the 
notations just employed above, by the length I — a. 
But then the velocity of the engine, corresponding 
to the real vaporization of all the water consumed 
by the boiler, would have been increased in the ratio 

' ; and in consequence the effective vaporiza- 

I '^ a. 

tion would have been diminished in the ratio — - — • 

The calculation performed with this new effective 
vaporization, would then have given for the engine 



OP THB LEAD OF THE SLIDE. 459 

a velocity less in the same ratio ; and in fine, to 
take account of the lead of the slide, it would have 
been necessary to multiply that velocity by the ratio 

— - — • Hence we should thus have fallen back on 

the same velocity which we obtained more simply 
by the method followed ; and for this reason, con* 
sidering besides how small the lead was, in the 
engines submitted to experiment, we preferred not 
to let those details figure in the calculation. 

In the experiments of Chapter XII., and in all 
the calculations of velocity made from our deter- 
minations, on engines having but little lead of the 
slide, it becomes needless then to enter into the con- 
sideration of the lead. But the engine Vesta, as we 
have said above, forms an exception in this respect. 
In effect, there existed in that engine a peculiar 
disposition which admitted of changing the lead of 
the slide at pleasure ; and while the engine was 
ascending the inclined plane of Whiston^ which was 
the moment when its efiective vaporization was cal- 
culated, the lead of the slide for the suppression of 
the steam had been reduced to f inch, whereas during 
the rest of the trip that lead had been fixed at ^ 
inch. The eff^ective vaporization of the engine is then 
determined as comprehending a lead of only f inch 
instead of ^ inch ; and as the former of these two 
leads reduces the stroke of the piston 1*50 inch, 
while the latter reduces it 3*35 inches, it becomes 
necessary, in order to take account of this difference, 



460 CHAPTKR XVI. 

to calculate the velocities of that engioe by taking 
the effective stroke of the piston at 12*65 inches, 
instead of 14*50 inches, as it was ¥rith the lead of f 
inch. This we did in calculating the velocities of 
that engine, and had we not had regard to this cir- 
cumstance, the calculation would have given about 
3 miles less on each of the velocities of the engine. 

From what has just been seen, the lead of the 
slide augments the velocity of the engine with a 
given load, and consequently its useful effect with 
that load Therefore, as the lead of the sUde shall 
be augmented, the useful effect will augm^it at the 
same time, and this augmentation will continue till, 
by reason of the lead, the effective stroke of the pis- 
ton is so much reduced, that the given load becomes 
a mcucimum load for the engine with that stroke. 
Beckoning from this point, the lead of the slide, and 
consequently the useful effect of the engine with the 
given load, admit of no further augmentation, since 
any further increase of the lead, or, in other words, 
any further diminution of the effective stroke of the 
piston, would render the engine incapable of draw- 
ing the desired load. 



Sect. III. Of the effects of the lead of the slide on 
the maximum load of which the engine is capable. . 

The advantages of the lead of the slide, which we 
have just noticed, are very important, since they 
consist in augmenting the velocity of the engine 



OF THE LEAD OF THE SLIDE. 461 

with a given load, or, in other words, its useful 
effect for a given vaporization, which impUes the di. 
minishing of its consumption of fuel for determined 
effects. These advantages are produced in the in- 
verse proportion of the lengths of the cylinder 
which are filled with steam at each stroke of the 
piston, and are therefore perfectly analogous to 
those which would result in the engine from an 
actual diminution of the stroke of the piston. 
But they are attended with a disadvantage which it 
is necessary to notice here, and which would equally 
occur in the case of an actual diminution of the 
stroke of the piston. The disadvantage consists in 
this, that the maximum load which the engine is 
capable of drawing becomes less at the same time ; 
so that, for the producing of certain effects, it may 
be advantageous to diminish, or even altogether to 
suppress, the lead of the slide. 

To be convinced of this fact, it suffices to observe 
that at the moment when the piston reaches the 
point which corresponds to the lead of the slide for 
the suppression of the steam, the motive force is 
suppressed ; and that, when the piston, continuing 
its stroke in virtue of its acquired velocity, arrives 
at the point which corresponds to the lead for the 
admission of the steam, it not only receives no fur- 
ther impulse in the direction of the motion, but 
suffers an opposition from the motive force itself, 
then let in against it. Now the piston cannot stop ; 
it must finish its stroke. It is therefore obliged to 



462 CHAPTER XVI. 

drive back the new steam which obstracts its way ; 
and as it consumes in overcoming the obstacle a 
quantity of work equal to that which this steam 
would have communicated to it, it follows that 
through the space yet remaining to traverse, there 
is destruction of the force previously acquired on an 
equal length of the cylinder. Thus, representing by 
a and fi the two portions of the stroke of the piston, 
which correspond to the two leads for the suppres- 
sion and admission of the steam, we see that the 
effect of the motive force, for the definitive motion, 
is now produced only on the length of the stroke, 
diminished first by a and afterwards by /8, or that 
there really remains, for the effort exerted by the 
engine, a stroke equal only to Z — « — )8. 

It will be remarked, indeed, that at the moment 
the steam is intercepted and the waste steam-port 
open, the motive force of the motion is not sup- 
pressed instantaneously, and that on the opening of 
the opposite port, the motive force is not let in 
instantaneously in the opposite direction ; for, as the 
steam requires a certain material time, either to 
escape firom above the piston, or to penetrate on the 
opposite side of it, it follows that during its efiiux 
by the blast-pipe, that steam does not entirely cease 
to exert an effort on the piston; neither, during its 
admission against the motion of the piston, has it, 
from the first, all the pressure of which it is capable 
to resist it. Moreover, during this suppression of the 
motive force in one direction and its introduction in 



OF THE LBAD OP THE SLIDE. 463 

the other, it will be remarked that the piston is very 
near the end of the cylinder, which occasions its 
action on the crank, that is, its action to produce or 
retard the motion of the engine, to be nearly null. 
From these two circumstances then it results, that 
the loss of motive force on the length a of the stroke 
of the piston, and its introduction in the opposite 
direction on the length fi of the same stroke, are but 
partial ; but calculating approximativdy, the effects 
of the engine may nevertheless be computed in 
supposing the effective stroke i^educed to the length 

Now, referring to the expression of the maximum 
load that the engine can draw (Chap. XII. Art. II. 
Sect. II.), we recognise that the more the quantity I 
diminishes, that is, the shorter the stroke of the 
piston becomes, the more the corresponding value 
of the load diminishes. Moreover, while the motive 
force is exerted only on the length Z— «— )8, the 
resistance of the load continues nevertheless to be 
exerted on the total length I of the stroke. From 
this fact then results a new disadvantage to the 
power, that is to say, a new diminution of the 
maximum load; and consequently, by these two 
causes, the extreme load of which the engine is 
capable wiU be by so much the less as the lead of 
the sUde is greater. 

To recognise by direct experiment to what degree 
the maximum load of an engine may be diminished 
by the lead of the slide, we undertook a series of 
experiments on the subject with the engine Vesta. 



464 



CHAPTER XVI. 



By a peculiar disposition, due to Mr. J. Gray, one 
of the engine-builders of the Liverpool and Man- 
chester Railway Company, this engine could, without 
interrupting its progress, be regulated for different 
leads of the slide, so that, with the same load and 
on the same ground, the effect of those different 
changes might be tried. They were produced by 
means of three notches, more or less advanced on 
the eccentric, and on which the driver might be 
brought at pleasure by means of a lever. The total 
range of the slide was 3*38 inches, and the three 
notches gave the following leads of the slide : 



1st notch 



2nd notch 



drd notch 



r lead of suppression 
\ lead of adinission 

r lead of suppression 
\ lead of admission 

r lead of suppression 
\ lead of admission 



4 inch. 



t 

T 



V 

5 

T 



To render the differences more sensible, it was 
between the first and the third of these positions of 
the slide that we endeavoured to obtain a com- 
parison. Consequently, on the 16th August, 1834, 
in the morning, and on the same day in the evening, 
the engine having been brought to the foot of the 
incUned plane of WhistoUy inclined ^, first with a 
train of 20 waggons, and afterwards with a train of 
8 waggons, every one of which had been previously 
weighed, a number more or less of these waggons 
was detached successively, and with each of these 
loads the greater and the lesser lead were succes- 
sively tried. The results of these trials are pre- 
sented in the following Table. 



OF THB LEAD OF THE SLIDE. 



465 



8 

■S 



«1 



•s 



1 



I 

I 






I 

lit 



•A 



t4 



W9 lO 

■ • 



I 

•ON 

1 

> 



I 



11 ^ 



11 



s 



"S 



1 









s. s. 



5 

•a 

a 

1 1 



I 

S 



OO 09 






QD 






Hi 



•g. 



s. 



s 
5 



QD CO 

00 Oi 

^ eo 






U3 









lid 

•a 



fill 

CO 02 09 O 



lA QD lO *A 

p CO il» O 

Ok ^ CO c« 

CO CO CO CO 



»J a K £;^ > p 



•M to 

M 
•I 



I i i 

<^ ? s ? 

iO 00 (-^ eo 



I 

'B 



«• d 



S "8 

1 1 1 f 1 1 



1 1:1 I 



g 

^ 



2h 



466 CHAPTER XVI. 

From these experiments it appears, that all the 
eDgine could do, with the leads of ^ and |- inch, 
was to draw a load weighing 32*05 tons ; and that 
with the leads of f and ^ inch it could, with the 
same pressure in tlie hoiler, draw a load of 39*05 
tons. Taking into the account the gravity of the 
train and engine on the plane inclined ^, these two 
loads are equivalent to 212 and 248 tons on a level. 
Thus the maximum load of the engine was reduced, 
by the lead, about ^, which may become important 
under certain circumstances. 



Sect. IV. Of the manner of regulating the lead of 

the slide. 

The preceding researches make known the effects 
of the lead of the slide, either on the velocity, or on 
the maximum load of the engine. We are then to 
be guided in this respect by the effects that are 
desired to be obtained from the engine. 

It is besides an easy thing to know the lead of 
the slide, and to regulate it at the point that may be 
thought proper. 

After having opened the door of the smoke-box 
situated under the chimney, and taken off the top 
of the slide valve box, so as to uncover the slides 
and observe their motion, the engine must be gently 
pushed forward on the rails, by hand, till the crank 
of the axle lies perfectly horizontal. 

At this moment the piston is at the end of the 



OF THE LBAD OF THE SLIDE. 467 

cylinder. Measuring then the quantity by which 
the slide now opens the steam-port/ we have the 
lead of the slide. 

If it be desired to diange the lead, the crank 
must be retained in the same position, and detaching 
the driver which is fixed to the axle only by a stop 
screw, the eccentric must be turned by hand till 
the slide, which moves at the same time, shall have 
opened the steam-port the desired quantity. Then 
the driver is to be refixed so as to hold the eccentric 
in that position. This operation being ended, it is 
plain that every time the crank shall Ue horizontally 
or the piston be ready to begin its stroke, the slide 
will be found to open the steam-port the proper 
quantity. 

We have said, that to bring the crank horizontal, 
it is in the forward direction that the engine must 
be pushed. The motive of this distinction is, that 
all the joints be tightened in the same manner as 
they are in the progressive motion of the engine. 
It is necessary also to bear in mind that these joints 
will be still more tightened, and the lead of the 
slide somewhat reduced, when the engine has to 
sustain the tension produced by a considerable 
load. 

Another attention is necessary before giving the 
lead, or measuring it, and this is to ascertain that 
the slide has an equal play between the three ports 
of the cylinder; that is to say, that in its two 
extreme positions it is equally distant from the two 



468 CHAPTER XVI. 

sides of the middle or wagte steam-port. Otherwise 
the lead of the slide would not be equal in the two 
motions of the piston. This defect, if it exist, is 
easily corrected by loigthening or shortening the 
eccentric rod as may be required. This rod is pur- 
posely formed of two parts (figs. 9 and 10), ter- 
minated by a rig^t and left screw, and joined by an 
adjusting4x>x E. When the box is turned, for 
instance, to the rig^t, the two screws tighten and 
the rod shortens. If on the contrary it is turned to 
the left, the two 8cre¥r8 become less ti^t and the rod 
lengthens. 

The r^ulation of the slide then is an easy ope- 
ration. 

The lead of the slide may, moreover, be changed 
with tolerable exactitude without opening the engine. 
It suffices to make beforehand on the axle, with a 
chisel and a hammer, two or three notches corre- 
sponding to two or three positions of the driver for 
given leads. These marks being once carefully de- 
termined as above, it is easy, by advancing the 
driver from one to the other, to make the slide pass 
from one lead to another greater or less. This is 
the means which we employed in some essays which 
we first made on this subject with the engine Leeds, 
and in which we successively changed the lead, 
from nil to ^ and f inch. 

The engine-men have several approximative ways 
of attaining the same end. They have remarked 
that, in general, a variation of ^ inch for the driver 



OF THE LEAD OF THE SLIDE. 469 

• 

in the opeDing of the eccentric, corresponds to a 
variation of \ inch in the lead of the slide. Thus, 
knowing the actual lead of the engine, they may, 
guided by this observation, diminish or augment 
that lead as much as they think proper. They 
attain their end also by loosening some keys or 
joints, so that the eccentric-rod no longer draws the 
rod of the slides immediately after it, but leaves, for 
instance, \ inch of play in the communication of 
the motion from the one to the other. It is readily 
conceived that, by this means, the slide will begin its 
motion ^ inch after the eccentric. If then the slide 
had before a lead of f inch, its lead afterwards will 
be but f inch. But this means and other similar 
ones are detrimental to the engine. 



CHAPTER XVII. 



OF INCUNED PLANES. 



Sect. I. Of the load on a level, which corresponds 
to the load on a given inclined plane, and vice 
versd. 

We have already shown, in Chapter VI., the means 
of computing the resistance opposed to the motion 
of the engines, by the gravity of the trains placed 
on incUned planes; but as many other questions 
occur relative to inclined planes on railways, we 
must here return to the subject, to solve the pro- 
blems which arise out of them. 

It often happens that an engine is observed to 
draw a certain load on a certain inclination, and 
to compare this work with that of another engine 
which would perform another task on a difierent 
inclination, it becomes necessary to refer each of 
these loads to the level. We shall therefore begin 
with this problem; that is to say, we shall seek 
the means of passing from a given load, drawn 
on a known inclination, to a train which would 
offer an equal resistance on a level; and reci- 
procally, from a known train, drawn on a level. 



OF INCLINED PLANES. 471 

to the load which, on a given inclination, would 
offer an equal resistance. 

Istly. Let us take the first case, and suppose the 
practical inclination of the plane to be expressed 

by-, that is to say, suppose its vertical elevation 

to be to its length measured along the plane, in 

the ratio of — Let M be the weight, in tons gross, 

e 

tender included, of the train placed on this inclined 
plane ; and let fc be the friction of the waggons per 
ton, expressed in pounds, as has been explained 
Chapter V. Rnally, let m be the weight, expressed 
in tons, of the engine which performs the traction. 

With these notations, it is clear that fcM will 
be the friction of the carriages of the train. More- 
over, since 1 ton contains 2240 lbs., the gravity of 
the train, plus the engine, will, as has been shown. 
Chapter VI., be expressed by 

2240 ^+"* . 
e 

Consequently, according as the engine has to ascend 
or to descend the plane, the total resistance it meets 
with from the train will be 

fcM ±2240^ + ^. 

e 

Th^*efore the train which, on a level, would offer an 
equivalent resistance, will have for its expression, 
when the motion is ascending, 



472 CHAPTER XVII. 

k e 



and when it is d 



tr^y^i^t'.ttit 



k e 

If, for instanoe, thane be a load of 50 tons, toader 
included, drawn up a plane inclined 9^, by an 
engine of the weight of 8 tons, it will be found that 
the equivalent load on a levd will be 86 tons ; and 
if the traction takes place in descending, the equi- 
valent load on a level will be no more than 14 tons. 

The case of descending trains offers no more dif- 
ficulty than that of ascending ones ; but it is to be 
remarked that when 

j^ 2240 M + m 

"" k e 

that \s to say, when the train , descends a plane 
whose inclination is expressed by 

1 k M 



e 2240 M + m 

the load which represents the resistance of the train 
will become null. Thus, on the plane whose in- 
clination we have just found, the friction proper 
to the waggons will be exactly counterbalanced 
by the gravity of the train augmented by that of 
the engine. On any plane of greater inclination, 
the resistance offered by the train, or the load M'', 
will be found negative; that is to say, that so far 



OF INCLINED PLANES. 473 

from opposing the progress of the engine, the wag- 
gons will tend on the contrary to urge it along the 
plane, with a force represented by the negative 
value thus obtained. 

When therefore the inclination of the plane, the 
weight of the waggons and that of the engine are 
known, the load M'\ which would offer an equi- 
valent resistance on a level, may immediately be 
found. 

2ndly. Suppose now that the result of an experi- 
ment have made known the load M^^ which a given 
engine can draw upon a level, and that it be desired 
to deduce therefrom the load M which the same 
engine could draw on a plane of a given inclina- 
tion; then the preceding equation, resolved with 
reference to M, will give, when the motion is as- 
cending, 

j^ eft M"- 2240 m , 

~ e& + 2240 ' 
and when it is descending, 

j^_ efcM^^ + 2240m 
~ eft -2240 

It will be easy then to find the load M required. 

If, for instance, we had found 86 tons for the load 
of an engine on a level, it would be deduced from 
thence that, on a plane ascending -^^^ and for an 
engine of the weight of 8 tons, that load would 
amount to 50 tons. 

It will again be remarked here, that if the inclina- 
tion of the plane in question be 



474 CHAPTER XVII. 



1 _ k M" 
e ~ 2240 ' m ' 

and if the motioa take place in ascending, the load 
which, on that plane, will correspond to the load 
M" on a level, will be null. This circumstance 
readily explains itself, on observing that we have 
then 

2240 m 1.,,, 

-r'-e = ^ ' 

which indicates that, by reason of the inclination of 
the plane, the gravity of the engine alone is equiva- 
lent to the load M'^ on a level, and consequently all 
that the engine can do will be to move itself up the 
plane. If the inclination be greater than that which 
we have just mentioned, a negative value will be 
found for the load of the engine, which would arise 
from the weight of the engine alone being already 
too great to represent the load M""' on a level. 

Finally, in the case in which the motion is de- 
scending, and in which 

1_ k 
€ ~ 2240' 

it will be found that the load of which the engine is 
capable is infinite; and in effect the inclination of 
the plane will be such, that the gravity of the wag- 
gons will compensate their friction, so that they will 
offer no resistance to the motion, and consequently 
the engine may draw an unlimited number of them. 
3rdly. Besides the two problems which have just 



OF INCLINED PLANES. 475 

occupied our attention, it may yet be required to 
determine what is the inclination on which a given 
load would be equivalent to another given load on a 
level. This research offers no difficulty; for the 
same relation obtained above, being resolved with 

reference to - gives, when the motion is ascending, 

1_ k M^^-M , 
e ~ 2240 ' M + m ' 

and when the motion is descending, 

1_ k M-M^^ 
e 2240 * M + m 

In these two expressions, M still expresses the load 
on the inclined plane, and M'^ the load on the level. 

Thus, for instance, if we seek on what inclination 
a load of 50 tons, drawn up an inclined plane by an 
engine of 8 tons weight, is equivalent to a load of 
86 tons on a level, we shall find the inclination of 
the plane to be ^^. 

It must however be observed, respecting the three 
problems which have just been considered, that the 
loads on a level, corresponding to loads on given 
inclinations, are equivalent to them only as ^ as 
they represent the traction and the gravity of those 
loads ; thus far then they may replace each other, 
but for this substitution to be exact, it must in no 
way affect the resistance of the air, which is, always 
to be valued by the number of waggons of the real 
load, and not by the number of waggons which 



476 CHAPTER XVII. 

would compose the fictitious load, if it were really 
to be drawn on a railway, practically and according 
to the ordinary manner of loading. 

For example, when a load on a level represents a 
load drawn up an inclined plane, it is clear that its 
weight must be greater ; and when it represents a 
load drawn down the plane, it will on the contrary 
have a less weight. In the former case, supposing 
the load on a level effectually prepared for convey- 
ance, it would require a greater number of carriages 
than the real load, and in the latter case, it would re- 
quire a less number. If then instead of computing 
the resistance of the air according to the number 
of carriages in the original load, it were valued ac- 
cording to the carriages which the transformed load 
supposes, the two loads thus considered would no 
longer offer an equal resistance. When therefore 
we say that two loads are equivalent to each other, 
it is not to be understood that they can, always and 
absolutely, replace each other, but merely that it is 
possible at the same velocity and with the proviso 
mentioned above. 



Sect: II. Of the velocity of locomotive engines on 

inclined planes. 

When a locomotive engine draws a train up an 
inclined plane, its velocity is necessarily diminished, 
and on the contrary its velocity is augmented when 
the engine draws its load down the plane. To be 



OF INCLINED PLANES. 477 

enabled then to form a complete judgment of the 
influence of inclined planes on railways, it is neces- 
sary to examine within what limits these effects of 
diminution and increase of velocity are produced. 
For this reason we are now about to consider the 
motion of the engines, in ascending and in descend- 
ing inclined planes. 

When a locomotive engine ascends an inclined 
plane, its load immediately becomes greater, because 
the gravity of the train on the plane is added to 
the friction of the waggons. One would then be in- 
duced to think that the velocity must diminish in 
a degree nearly proportionate; but that is not the 
case, because, as the velocity of the engine di- 
minishes, the resistance of the air diminishes very 
rapidly, since it varies in the ratio of the square 
of the velocity ; and consequently there remains in 
the engine, so much the more force to apply to the 
traction of the load. For the same reason, the 
velocity, in descending inclined planes, does not 
increase indefinitely, as might be thought at a first 
glance. 

This will easily be recognised on recurring to the 
practical formula which we have presented in Article 
III. of Chapter XII., for determining the velocity of 
the engine, with a given load and on a known in- 
clination, namely : 

784 S 

V=z _ _- . 

(1-hd) [(6±y)M±5rm-hiit;2j -hF-h ?gi (2736-hyt;) 



480 CHAPTER XVII. 



Sect. III. Of the velocity of descent of trains^ an 
inclined planes where no use is made of the force 
of the engine. 

The researches which have just engaged us are 
relative to the ascent and descent of planes, on 
which the force of the engine is used to produce 
the motion of the train. This case invariably 
occurs in all questions of ascent, but it obviously 
does not always in questions of descent. In effect, 
the latter may be divided into three classes : 

1st. Inclinations on which the gravity is less than 
the friction, and whereon the train could not 
advance without the help of the engine ; 

2nd. Inclinations on which the gravity exceeds 
the friction, and whereon the trains would 
descend of themselves, but with a velocity 
less than what the work requires; 

3rd. Inclinations on which the gravity so much 
exceeds the friction, that the trains would 
acquire too great a velocity during their de- 
scent, if they were not restrained in their 
motion by the use of the brake. 

The first case is evidently comprised among those 
which have been treated of in the preceding sec- 
tion ; and it is the same with the two others, when- 
ever it is thought prefer to use the force of the 
engine, notwithstanding the inclination of the plane. 



OF INCLINED PLANES. 481 

In the second case, there may occur a problem 
which we have not yet noticed : it is that of finding 
what vaporization the engine ought to have, or to 
apply, in order to communicate to the descending 
train a determined velocity. This problem would 
be solved by taking equation (7), Chapter XIII. 
Sect. II., which gives the effective vaporization 
of the engine for desired effects, and substituting 
in it for the friction, gravity, &c., the data proper 
to the inclined plane in question. It can therefore 
offer no difficulty, and we shall dwell no longer 
on it. 

In the third case, it may be required to find what 
velocity the trains would attain of themselves during 
their spontaneous descent on the plane, and what 
effort the brake ought to apply, to reduce their 
velocity within certain fixed limits. This is the 
object of our inquiry at present. 

When the inclination of a plane is such that, 
aided by the steam, the waggons would be liable to 
acquire a greater velocity than would be thought 
consistent with the safety of the passengers or the 
preservation of the engine and carriages, the engme- 
men suspend the action of the engine entirely. Then 
the motion is nothipg more than the result of the 
natural gravity of the train on the declivity, and it 
is easy to obtain its valuation. 

Suppose, in effect, the train to reach the summit 
of the plane with the velocity, already considerable, 
which results from the prior action of the engine ; 

2i 



480 CHAFTBR XVII. 



Sect. HI. Of ike velocity of descent of Irakis, on 
imclimed pUmet where no use is made of the force 
of the engine. 

The researches which have just engaged us are 
rdative to the ascent and descent of planes, on 
which the force of the engine is used to produce 
the motioQ of the train. This case invariably 
occms in all questions of ascent, but it obviously 
does not alwajrs in questions of descent. In effect^ 
the latter may be divided into three classes : 



1st. Indinations on which the gravity is less than 
the friction, and whereon the train could not 
advance without the help of the engine ; 
2nd. Indinations on which the gravity exceeds 
the fiiction, and hereon the trains would 
descend of themselves, but with a velocity 
less than what the work requires; 
3rd. Indinations on which the gravity so much 
exceeds the friction, that the trains would 
acquire too great a velodty during their de- 
scent, if they were not restrained in their 
motion by the use of the brake. 

The first case is evidently comprised among those 
whidi have been treated of in the preceding sec- 
tion ; and it is the same with the two others, when- 
ever it is thought proper to use the force of the 
engine, notwithstanding the inclination of the plane. 



^ 



OF INCLINED PLANES. 



481 



In the second case, there may occur a problem 
which we have not yet noticed : it is that of finding 
what vaporization the engine ought to have, or to 
apply, in order to communicate to the descending 
train a determined velocity. This problem would 
be solved by taking equation (7), Chapter XIII. 
Sect. II., which gives the effective vaporization 
of the engine for desired effects, and substituting 
in it for the friction, gravity, &c., the data proper 
to the inclined plane in question. It can therefore 
offer no difficulty, and we shall dwell no longer 
on it. 

In the third case, it may be required to find what 
velocity the trains would attain of themselves during 
their spontaneous descent on the plane, and what 
effort the brake ought to apply, to reduce their 
velocity within certain fixed limits. This is the 
object of our inquiry at present. 

When the inclination of a plane is such that, 
aided by the steam, the waggons would be Uable to 
acquire a greater velocity than would be thought 
consistent with the safety of the passengers or the 
preservation of the engine and carriages, the engine- 
men suspend the action of the engine entirely. Tboi 
the motion is nothipg more than the result of^ 
natural gravity of the train on the decliviiy, 
is easy to obtain its valuation. 

Suppose, in effect, the train to readi (Ar 
of the plane with the velocity, alreadr 
suits from the prior actkm 



.tu;. 





/ 



i 




A 



k^ 



482 CHAPTER XVII. 

it will first begin its motion on the plane with that 
same velocity, and will tend to augment it more 
and more, by reason of the constant action of the 
gravity. But it is clear that, in this case, the 
motive force will be nothing more than the excess 
of the gravity, above the friction of the waggons 
augmented by the friction of the engine; and the 
resistance will be precisely the resistance of the air. 
So long as the motive force predominates over the 
resistance, the motion will continue to accelerate; 
but as the motive force is constant, and as the 
resistance of the air on the contrary increases 
rapidly, there will be a point at which those two 
forces will become equal ; and from that moment the 
motion will be uniform. Considering, in Chapter V., 
the motion of bodies committed to gravity on in- 
clined planes, we have shown that this uniformity 
of motion will establish itself at the end of a limited 
time. 

If then the train be supposed to Jiave attained 
that uniform motion, the resistance of the air will 
be equal to the motive force. Now the motive force 
is known, since it is no other than the excess 
of the gravity above the frictions. Therefore the 
excess of the gravity above tbe frictions will give 
also the intensity of the resistance of the air during 
uniform motion ; and consequently we may thence 
deduce the velocity of that motion, or the velocity 
which the train will necessarily acquire afler a 
limited time of its descent. Hence, neglecting the 



OF INCLINED PLANES. 



483 



difference which existed, at the commencement of 
the motion on the plane, between the velocity of 
the train resulting from the previous action of the 
engine, and its definitive velocity residting from 
gravity, we may take the uniform velocity which we 
have just determined, as that of the whole passage 
of that descent. 

If, for example, we consider a train of 9 coaches 
and tender, weighing 50 tons, preceded by an engine 
weighing 8 tons, and suppose it placed on a plane 
inclined xhf, the gravity of the train and engine 
Yrill be 866 fts., the friction of the waggons will be 
300 lbs., and that of the engine 100 fcs. nearly. 
Thus the motive force, and consequently also the 
resistance of the air during the motion, will be 
466 lbs. Now the train offers to the resistance of 
the air an effective surface of 170 square feet. 
Hence the resistance of the air per square foot of 
surface, will be 2*74 lbs.; which gives for the ve- 
locity of the motion 31*94 miles per hour. If a 
similar calculation be made, for different cases, the 
following Table will be formed : 

Velocity of descent of trains left to themselves on inclined 

planes. 



Deaignatioii of the tram. 


Maximam velocity of the 

train, in miles per hour, the 

inclination of the plane being: 


vvv 


rsff 


ToJf 


Train of 50 tons, tender included 
Train of 100 tons, tender included 


23-40 
26-21 


31-94 
3507 


44-36 
48-12 



484 CHAPTER XVII. 

Such are then the velocities the trains would attain 
when abandoned to their own weight; but upon 
railways a maximum velocity is fixed for the descent 
of inclined planes, and that velocity is determined 
with a view to the preservation of the railway and 
carriages. If then we suppose that the greatest 
velocity of descent on inclined planes has been 
fixed at 26 miles per hour, as on the Liverpool 
and Manchester Railway, it is plain that in the 
different cases which we have just treated, the 
engine-men will be obliged to use the brake, to 
reduce the velocity to 26 miles per hour. Now as 
the resistance of the air against a train of 10 
coaches and the engine, at the velocity of 26 miles 
per hour, is 309 fts., the effective motive force must 
obviously, in all the cases, be reduced to that rate. 
In practice, this effect will be produced by guess 
and trial, by tightening the brake more or less ; but 
it is easy to determine the friction which, in each 
case, the brake ought to exert in order to obtain the 
velocity desired. If, for instance, we consider the 
train of 50 tons descending a plane inclined yfg^, 
the effort of the brake must obviously be 466—309 
= 157 lbs., and the calculation will be the same for 
any other case. 

These examples show that, whether the force of 
the engine be employed wholly or partially, or the 
trains be left to themselves, or their speed be 
moderated by the application of the brake, it will be 
easy, in all cases, to determine their velocity on the 
inclined planes. 



OF INCLINED PLANES. 485 

The same Examples show that exaggerated fears 
have been entertained, in France, of the dangers 
which might result from the occurrence of declivities 
on railways, and that it was carrying the precaution 
too far to prohibit, in an almost absolute manner, 
inclinations greater than the angle of friction, on 
account of the danger to which they seemed to 
expose the descending trains. This apprehension 
was founded on the idea that, by the very fact of 
the trains rolling spontaneously down the planes, 
they might accelerate their velocity almost inde- 
finitely. But the osculations which we have just 
presented prove that, even though the brakes should 
happen to give way, the velocity of descent of a 
train of 100 tons, which is one of the heaviest in 
use, would not exceed 48 miles per hour on an 
inclination of you. Now this velocity is itself com- 
prised within the limits that powerful engines attain 
with light loads, and the Government has not as yet 
deemed it necessary to interfere in this respect. 
Besides, we have said that on rapid descents the 
brake is applied ; and for above twelve years that the 
Liverpool and Manchester Railway has existed, the 
velocity of the heaviest trains has invariably been 
reduced to 22 and 26 miles per hour, on planes 
inclined ^ and ^, without any accident resulting 
from that cause. We hope then the conviction will 
prevail, that the only inconveniences attendant on 
declivities consist in the surplus of work they 
impose on the engines ; and in that respect, it is 



486 CHAPTER XVII. 

proper to leave to the companies who undertake 
railways, the care of judging whether it is more 
advantageous for them to make a tunnel or go 
round a hill, rather than crossing it by means of an 
inclined plane. But by refusing them the faculty of 
employing the latter means, it has often happened 
that expenses have been imposed on them, so heavy 
as to amount almost to a complete prohibition of 
the establishment of the railway. 



Sect. IV. Of the duration of the trip, and of the 
average velocity of the engines^ on a system of 
sixcessive inclinations. 

• 

In the case of a train drawn on a railway which is 
either level, or of a uniform inclination, there can 
be no difficulty in finding the duration of the trip 
from one point of the railway to another. In effect, 
as the time employed by a body in traversing a 
given space with a uniform motion, is equal to the 
space traversed, divided by the velocity of the 
motion, it will suffice, first, to determine the ve- 
locity of the engine with the desired load, and then 
to divide the whole length of the way by the ve- 
locity of the engine, and the result will be the time 

sought or the duration of the trip. 

■ 

For example, if an engine is to traverse a space 
of 30 miles, with a velocity of 10 miles per hour, 
the duration of the trip of 30 miles will be 

— = 3 hours. 



OF INCLINED PLANES. 487 

But if the line to be traversed consist of a series 
of ascents and descents of various inclinations, the 
question will become more complex, without how- 
ever presenting more difficulty. 

In this case, the velocity of the engine, Ynth the 
given load, on each of the inclinations to be tra- 
versed, must be sought, either by the formula 
(1 bis). Chapter XII., or by the means indicated in 
the preceding section ; then the separate lengths of 
the inclinations must be divided, each by the re- 
spective velocity of the engine, which will give the 
time employed in traversing each inclination ; and 
the sum of all the results thus obtained will be the 
total duration of the trip. Finally, dividing the 
whole distance by the total duration of the trip, the 
quotient will be the average velocity of the trip. 

If, for example, it were found that the engine 
would perform 10 miles with the velocity of 10 
miles per hour, 10 miles with the velocity of 20 
miles per hour, and 10 miles at the velocity of 30 
miles per hour, the total time of performing the 
30 tniles would be 

;0+ 10+ 10= 1-83 hour; 
10 ^ 20 ^ 30 

and consequently the average velocity on the whole 
distance of 30 miles would be 

30 

= 16*4 miles per hour. 



1-83 

« 

In general, if the successive lengths of the inclined 



488 CHAPTER XVII. 

planes to be traversed, be expressed by Lj, L,, &c., 
and the respective velocities of the engine on those 
inclinations by V,, V„ &c., the time of performing 
the whole distance will be 

and the average velocity of the trip will be 

L| + L a + &c. 

%+^- 

This question then can offer no difficulty. 

Among the applications relative to- this question, 
we may have to consider a series of ascents and de- 
scents between two points on a level, with a view 
to determine what disadvantage there vfUl be, with 
r^ard to the duration of the trip, and for an engine 
and train of known weight, in following the undu- 
lating line, instead of the straight and level line 
which would join the two extreme points. This 
problem occurs whenever, in projecting a railway, it 
becomes necessary to choose between cutting through 
a hill and crossing it by means of inclined planes. 

In this case, the calculation will be similar to the 
preceding. The velocity corresponding to the pas- 
sage of the train over each inclination must be found 
first, and after having deduced from it the time 
employed in traversing all the inclinations, that time 
must be compared with the time the engine would 
require, according to equation (1 bis), to perform 



OF INCLINED PLANES. 



489 



the straight and level Une which would join the 
extreme points. 

If, for example, it be desired to know the time of 
traversing a total distance of 20 miles, and the 
average velocity of the same engine, which has been 
noticed in Sect. ii. of this chapter, with its load of 
56 tons gross, tender included, in following either a 
line entirely level, or a line of the same length, but 
consisting of two equal and contrary incUnations, 
referring to the velocities already obtained in Sect. 
II., we shall form the following Table : — 



Time of traversing 20 milesy and average velocity of a loco- 
motive of 65 cubic feet of vaporization, with a load of 
56 tons gross, on a system of equal ascents and descents. 



• 

Object of calculation. 


Designation of the line to be traversed. 


10 miles 

on a level 

and 

10 miles 
on a level. 


10 miles 

ascending 

and 

10 miles 
descending 


10 miles 

ascending 

and 

10 miles 
descending 


10 miles 

ascending 

and 

10 miles 
descending 


Time of traversrag 20 
miles, in minutes . 

Average velocity of 
the trip, in miles 
per hour 


j 47-65 

Us- 10 


48-36 
24-81 


48-69 
24-64 


55-66 
21-56 



We see by these results, that on a system of 
equal ascents and descents, compared with a level 
line of the same length, the engine will always be at 
a disadvantage with respect to the average velocity, 



490 CHAPTEE XVII. 

or the duration of the whole trip, 4since it here ap- 
pears that the velocity, which was 25' 10 miles per 
hour on a level, reduced itself successively to 24*81, 
24*64, and 21*56, and the time of performing the 
whole distance increases in a corresponding manner, 
according to the system of planes over which the 
engine has to pass. 

It will be remarked at the same time, that it 
would be quite inaccurate to take, as the average 
velocity of the passage of the two inclinations, the 
mean between the two velocities which we have 
obtained in Sect, ii., for the ascent and descent 
of those inclinations, because those two velocities 
are not maintained by the engine during equal 
times. 



Sbct. V. Of the average load of the engineSy during 
their passage over a system of successive planes. 

When an engine ascends and descends several 
successive inclinations, its load varies considerably, 
since the gravity of the train now increases, qow 
diminishes the original resistance of the train on a 
level. It is necessary then to be able to calculate 
the average load which results from these variations 
during the whole time of the trip. 

For this purpose it will suffice first to calculate, 
by the means above indicated, the load on a level 
which corresponds to the traction of the train over 
each plane, and the time of traversing each respec- 



OF INCLINED PLANES. 491 

tive plane, that is to say» the time during which the 
engine has to draw that load. Then, multiplying 
each load by the time during which it is applied to 
the engine, taking the sum of all these products, 
and dividing that sum by the total time employed 
in traversing all the planes, the result will be the 
average load of the engine during the trip. 

Suppose, in effect, the question concern a system 
of two inclined, planes : one on which the load is 
equivalent to 1 50 tons, and which requires 3 hours 
of time; the other on which the load is equiva- 
lent to 50 tons, and which requires 1 hour of 
time. It is clear that during the first hour the load 
of the engine is 1 50 tons ; during the second and 
third, the load is still 150 tons; and during the 
fourth hour, the load is 50 tons. Hence, during 
each successive hour of the duration of the trip, the 
loads will be 

150 tons 
150 
150 
50 



500 tons ; 

and as the total trip has had a duration of 4 
hours, we see that the average load of the engine 
during the whole trip, or per hour of work, will 
be 

^=125 tons. 



492 CHAPTER XVII. 

To obtain, therefore, the average load of the engine, 
each effective load must be multiplied by the time it 
is applied to the engine, the sum of all these pro- 
ducts must be taken, and 'finally that sum divided 
by the total time of the trip. 

Thus, in general, expressing by Mi, M,, &c., the 
successive loads of the engine on different planes, 
by Li, La, &c., the respective lengths of the planes, 
and by V„ V,, &c., the corresponding velocities, 

h h &c 

will be the times employed in traversing each of the 
successive planes ; and 

will be the average load of the engine during the 
whole trip. 

If the line in question consist of ascents and 
descents traced between two points on a level, or of 
ascents and descents counterbalancing each other, 
the average load of the engine during its passage 
over those inclinations, will always be greater than 
it would be on the level line which would join the 
two extreme points. In effect, if we first calculate 
the effective loads, or the loads reduced to a level, 
which correspond to the passage of an engine of the 



OF INCLINED PLANES. 



493 



weight of 8 tons, drawing a train of 56 tons gross, 
tender included, over divers given inclinations, we 
shall obtain the following results : — 

Effective loads of an engine of 8 tons weighty drawing a 
train of 56 tons on divers given inclinations. 



Direction of the 
motion. 


Effective load of the engine, in tons, the 
inclination of the plane being : 





-shv 


tIt 


^ 


Ascending 
Descending 


56 
56 


95-83 
16-17 


10917 
2-83 


215-33 
-103-33 



Then, recurring to the duration of the passage of 
the same engine with its load over the different 
planes, as obtained in the preceding section, and 
proceeding, as we have just indicated, to find the 
average load of the engine in ascending and de- 
scending different planes successively, we shall ob- 
tsdn the following Table : — 

Average load of an engine of 8 tons weighty traversing ^ with 
a train of 56 tons gross, a system of given ascents and 
descents. 



Object of calcu- 
lation. 



Average load, 1 
in tons gross J 



Designation of the line to be traversed. 



10 miles on 
a level and 
10 miles on 
a level. 



56 



10 miles as- 
cending and 

10 miles 
descending 



6104 



10 miles as- 
cending and cending 

10 miles 
descending 



65-21 



10 miles as 
and 
10 miles 
descending 

TtT' 



127-37 



494 CHAPTER XVII. 

It appears, from these results, (hat there is always 
a disadvantage in laying down a railway according 
to a line of ascents and descents, instead of tracing 
it according to the horizontal line which would join 
the extreme points ; also that this disadvantage will 
augment as the planes to be traversed are more 
inclined, and that it will always subsist even for 
planes less inclined than the angle of friction. 

It will be remarked, that had we merely taken the 
mean between the ascending and the descending 
loads, on the different planes^ we should have had 
56 tons, in every case, for the average load of the 
engine. But that calculation would have been 
faulty, since, if we take as an example the two 
planes inclined 4^, the engine has to draw the load 
of 109' 17 tons during 28*56 minutes, and the load 
of 2*83 tons during only 20* 13 minutes ; and simply 
taking the mean of the two loads, is by the fact 
supposing that the two planes are traversed in equal 
times. 

Through not having made this distinction, some 
engineers have thought that, as long as the inclina- 
tions did not exceed that on which the waggons 
run of themselves, the traction of the engines re- 
mained the same as if the line were perfectly level. 
As their practice was to compute the average load 
by taking the mean between the ascending and the 
descending loads, they concluded that the surplus of 
traction in the one case was compensated by its 
diminution in the other ; and thence the name of 



OF INCLINED PLANES. 495 

normal inclinations was given to inclinations less 
than the angle of friction. But it is plain that no 
inclination on a railway can be called normal, since 
all slants, of whatever inclination they may be, are 
disadvantageous in all cases. We have, in effect, 
seen in the preceding section, that on a system of 
ascents and descents of any kind, the average velo- 
city of the engines with the same load is diminished, 
or the time of traversing the same distance aug- 
mented ; we here see that, on the same system of 
planes, the average load of the engine per hour of 
work is increased. On the other hand, it is obvious 
that the useful effect definitively produced remains 
always the same, since it consists solely in the con- 
veyance of the load from one extremity of the line 
to the other. There can be no doubt, then, that the 
occurrence of ascents and descents on a railway is 
disadvantageous in all respects. 

Sect. VI. Of the quantity of work on a level, which 
corresponds to the conveyance of a given load, 
over a system of knoum inclinations. 

There is yet another research which necessarily 
presents itself with respect to railways consisting of 
a series of different inclinations ; namely, that of the 
quantity of work on a level, and at a Uke velocity, 
which corresponds to the total work executed by the 
engine during its trip. We mean to say that, when 
an engine traverses a system of various inclinations, 



496 CHAPTER XVII. 

it performs, in traversiog each of those inclinations, 
a certain quantity of work, which is measured by 
the traction required of the engine and the length of 
the inclination, or the distance on which that trac- 
tion is exerted. When the engine then has finished 
its trip, it has executed successively difierent quan- 
tities of work ; and the object proposed is to find 
the quantity of total work thus done by the engine, 
and to deduce therefrom the work on a level, which 
would be equivalent to it. 

This problem occurs whenever, after having ob- 
served the expenditure of fiiel of an engine, in 
traversmg a system of planes with a given load, it is 
required to deduce the expenditure of that fuel 
which corresponds to the traction of 1 ton 1 mile 
on a level. It is also the problem which occurs 
when, after having observed the expenses of main- 
taining and working the engines on a railway com- 
posed of ascents and descents, it is required to 
deduce what those expenses would be on a level 
line. 

To obtain the solution of this question, we must 
first seek the quantities of work successively done 
in the conveyance of the train on each inclination, 
and their sum will give the work executed in the 
whole trip. Comparing afterwards this work with 
that which would be done in drawing a ton 1 mile 
on a level, we deduce its expression in tons drawn 
1 mile on a level. 

Now, the force necessary to overcome the friction 



OF INCLINED PLANBS. 497 

of the waggons placed on the plane, is known. 
Moreover, dividing the total weight of the train, 
augmented hy that of the engine, and by that of the 
tender, if the latter have not been originally com- 
prised in the weight of the load, by the number 
which represents the inclination of the plane, we 
have likewise the gravity. We can therefore calcu- 
late the traction required of the engine during its 
passage over each plane, and multiplying that trac- 
tion by the distance on which it is exerted, we have 
the quantity of work performed during the passage 
of the inclination. Making successively a similar 
calculation for each plane, we may conclude the 
total work demanded of the engine during the whole 
trip ; and, finally, knowing that the draught of a 
ton 1 mile on a level requires a traction of 6 fts. 
1 mile of distance, or a quantity of work of 6 fts. 
raised 1 mile, we may definitively deduce the work, 
on a level, which corresponds to the total work of 
the engine. 

To simplify this calculation, instead of seeking 
immediately the definitive work required of the 
engine on each inclination, by virtue of the friction 
and the gravity, we may, which amounts to the 
same, calculate first the work performed in over- 
coming the gravity of 1 ton on each successive in- 
clination. Then, having once found this work, ex- 
pressed in pounds raised 1 mile, knowing also that 
a weight of 6 fts. is equivalent to the traction of 
1 ton on a level, we may immediately express it in 

2k 



496 CHAPTER XVII. 

it perforins, in traversing each of those inclinations, 
a certain quantity of work, which is measured by 
the traction required of the engine and the length of 
the inclination, or the distance on which that trac- 
tion is exerted. When the engine then has finished 
its trip, it has executed successively different quan- 
tities of work ; and the object proposed is to find 
the quantity of total work thus done by the engine, 
and to deduce therefrom the work on a level, which 
would be equivalent to it. 

This problem occurs whenever, after having ob- 
served the expenditure of fiiel of an engine, in 
traversing a system of planes with a given load, it is 
required to deduce the expenditure of that fuel 
which corresponds to the traction of 1 ton 1 mile 
on a level. It is also the problem which occurs 
when, after having observed the expenses of main- 
taining and working the engines on a railway com- 
posed of ascents and descents, it is required to 
deduce what those expenses would be on a level 
line. 

To obtain the solution of this question, we must 
first seek the quantities of work successively done 
in the conveyance of the train on each inclination, 
and their sum will give the work executed in the 
whole trip. Comparing afterwards this work with 
that which would be done in drawing a ton 1 mile 
on a level, we deduce its expression in tons drawn 
1 mile on a level. 

Now, the force necessary to overcome the friction 



OF INCLINED PLANBS. 497 

of the waggons placed on the plane, is known. 
Moreover, dividing the total weight of the train, 
augmented by that of the engine, and by that of the 
tender, if the latter have not been originally com- 
prised in the weight of the load, by the number 
which represents the inclination of the plane, we 
have likewise the gravity. We can therefore calcu- 
late the traction required of the engine during its 
passage over each plane, and multiplying that trac- 
tion by the distance on which it is exerted, we have 
the quantity of work performed during the passage 
of the inclination. Making successively a similar 
calculation for each plane, we may conclude the 
total work demanded of the engine during the whole 
trip ; and, finally, knowing that the draught of a 
ton 1 mile on a level requires a traction of 6 fts. 
1 mile of distance, or a quantity of work of 6 fts. 
raised 1 mile, we may definitively deduce the work, 
on a level, which corresponds to the total work of 
the engine. 

To simplify this calculation, instead of seeking 
immediately the definitive work required of the 
engine on each inclination, by virtue of the friction 
and the gravity, we may, which amounts to the 
same, calculate first the work performed in over- 
coming the gravity of 1 ton on each successive in- 
clination. Then, having once found this work, ex- 
pressed in pounds raised 1 mile, knowing also that 
a weight of 6 lbs. is equivalent to the traction of 
1 ton on a level, we may immediately express it in 

2k 



498 CHAPTER XVII. 

tons drawn 1 mile on a level. After having ob- 
tained this expression for each of the successive 
planes, nothing remains but to take the sum of 
these expressions, in order to have the total work 
resulting from the draught of 1 ton over all the 
planes of the whole line. Consequently, multi- 
plying this result by the number of tons which 
compose the total mass in motion, and adding to it 
the work done in overcoming the resistance of the 
air and the friction of the waggons, on the total 
length of the trip, we shall have definitively the 
work performed in the traction of the train over all 
the planes of the whole line. It is necessary only, 
before going any farther, to add here two observa- 
tions. 

Tlie furst is, that it is proper to distinguish the 
ascents from the descents, and, to that end, care 
must always be taken to give to the work done in 
overcoming the gravity, the sign plus for those por- 
tions of the Une which are to be ascended, because 
on those portions the gravity, and consequently the 
work which represents it, is to be added to the 
traction of the waggons; and the sign minus for 
those portions of the line which are traversed in 
descending, because on descents the gravity, on the 
contrary, comes in deduction of the work required 
of the engine, and is consequently to be subtracted. 
By this means, we have only to add, with their 
sign, all the quantities of work thus found, in order 
to deduce the definitive work done in overcoming 



OF INCLINED PLANES. 499 

the gravity of 1 ton on the whole line of inclina- 
tions. 

The second observation which we have to make is 
relative to planes more inclined than the angle of 
friction. It is known that on these planes the 
gravity exceeds the friction, so that the train might, 
in fact, continue its motion without the help of the 
engine. However, as for a railway enterprise it is 
not enough that the train move slowly onward, but 
it must assume and maintain the velocity fixed by 
the exigencies of the trade ; as, moreover, the train 
cannot run of itself at any velocity on a descent, 
unless the gravity be capable of overcoming not 
only the friction of the waggons but that of the 
engine, it follows, finally, that it is only on planes 
sufficiently inclined for the gravity to be equal to 
the ^um of the friction of the waggons, the friction 
of the engine, and the resistance of the air against 
the train at the desired velocity, that the effect of 
the engine can be dispensed with. 

According to the velocities in use on railways at 
the present day, 25 miles per hour may be con- 
sidered as the velocity generally adopted for a train 
of 10 carriages or 50 tons gross, exclusive of the 
tender, and about 20 miles per hour for that of a 
train of 20 waggons or 100 tons gross, exclusive of 
the tender. Admitting then these data, and taking, 
besides, 100 fts. for the friction proper to an engine 
of 8 tons, it appears that the inclinations on which 
it would be possible to suspend the action of the 



500 CHAPTER XVII. 

steam will be -^^ in the first case, and t^t ^^ ^^ 
second. It may then be admitted, on an average, 
that, on a well-kept railway adapted to ordinary 
velocities, with well-constructed carriages, the trains 
will of themselves acquire a sufficient velocity, when 
the inclination is -3^ ; so that on such inclinations 
the action of the steam may be entirely suspended. 
This premised, it is visible that in seeking the quan- 
tities of work done by the engine in traversing a 
system of divers planes, we must set down zero for 
all descending planes inclined -3^ or more ; that is 
to say, we must, for those planes, omit in the calcu- 
lation both the gravity of the mass and the friction 
of the waggons, since these two quantities mutually 
destroy each other. 

To give an example of this calculation, and to 
render the explanation of it perfectly clear, we will 
seek the quantity of work done by the locomotive 
engines of the Liverpool and Manchester Railway, in 
the conveyance of their load over the totality of the 
space which they have to traverse. As the calcula- 
tion relative to the gravity is performed much more 
commodiously by way of a Table, we will here pre- 
sent it under that form. The first column of the 
Table contains the successive lengths of the line, the 
second indicates the respective inclinations of each 
of those distances, the third gives the gravity of 1 
ton on the inclination considered ; the fourth and 
last contains the product of that gravity by the 
distance traversed, that is, the work done in over- 



OF INCLINED PLANES. 



501 



coming the gravity ; but, having been divided by 6, 
this work is transformed into tons drawn 1 mile on 
a level. 

Tlie signs placed before the numbers mark, as we 
have just said, the ascending or the descending 
planes. Thus the inclination f^^ is a descent in 
going from Liverpool to Manchester, and therefore 
the work corresponding to the gravity has the sign 
minus; but it is an ascent when the line is traversed 
in the opposite direction, which causes it, in that 
case, to have the sign plus. The gravity on the 
inclinations ^"^ and ^^-^ might have been neg- 
lected in this calculation, because in practice these 
inclinations may be treated as level Unes. 



Work done in overcoming the gravity on the Liverpool and 

Manchester Railway. 



Section of tbe railway, from 

LiTerpooI towards 

Manchester. 



Distances. 



miles. 
•53 
5-23 
1-47 
1-87 
1-39 
2-41 
6-60 
5-62 
4*36 

29-48 



Inclinations. 



d. 
a. 





1 



1 
TV 



d. 
d. 



Gravity of 1 
ton on the 
inclination 
traversed. 



tbs. 



2-04 
23 33 


2500 
•81 

2-64 

1-72 
•52 



Work done in overcoming 
the gravity of 1 ton 



From Liver- 
pool towards 
Manchester. 



tons 1 mile on 
a leveL 


-1-78 
-f5-71 



- -32 
-2-90 
+ 1-61 
+ -38 

+ 2-70 



tons 1 mile on 
a leveL 


-f 1-78 



From Man- 
chester 
towards 

liverpooL 



f» 




+5-79 
+ -32 
+ 2-90 
-1-61 
- -38 

+ 8-88 



502 CHAPTER xvir. 

This Table shows that the gravity of each ton of 
a train drawn from one end to the other of the 
Liverpool and Manchester Railway, requires from the 
engine, according to the direction of the motion, a 
quantity of work equivalent to 2*70 or 8'88 tons 
drawn 1 mile on a level. Ebcpressing then by M, 
the weight of any train, by m the weight of the 
engine, and by C the weight of its -tender supposed 
not included in the load Mj, the work done in over- 
coming the gravity of the train on the line, will be 

From Liverp. to Manch. . . 2*70 (M, -f- C -f m) tons 1 mile; 
From Manch. to Liverp. . . 8'88 (M, -f- C -f m) tons 1 mile. 

But on the other hand, laying aside the descents 
more inclined than -j^, on which the engines are 
not made to work, the distance performed by the 
trains is 28*09 miles from Liverpool towards Man- 
chester, and 28*01 miies in the contrary direction; 
and the friction of the carriages is to be overcome 
by the engine throughout the extent of this distance* 
Therefore, the quantity of work done in overcoming 
the friction of the carriages, for a load of M, -|- C 
tons drawn from one end of the line to the other, 
will be 

From Liverp. to Manch. . . . 28*09 (M, + C) tons 1 mile ; 
From Manch. to Liverp. . . . 2801 (M, -f C) tons 1 mile. 

Hence, finally, adding the work done in overcoming 
the gravity to that which is done in overcoming the 
friction, the total work performed by the engine, in 



OF INCLINED PLANES. 503 

the conveyance of the load Mi along the whole line, 
will be 

From Liverp. to Manch. . . 30'79 (Mj +C) +2-70 m tons 1 mfle. 
From Manch. to Liverp, . . 36-89 (Mi +C) +8*88 m tons 1 mile. 

In these expressions, m represents the weight of the 
engine effecting the motion. It is understood then 
that if the train is drawn by two or more engines, m 
is to be replaced by the weight of those different 
engines united. Similarly, if a train is helped in 
a part of the trip by an assistant engine, the above 
quantity of work must receive an addition, corre- 
sponding to the gravity of the assistant engine and 
its tender, on the portion of the line which it has to 
traverse, and to the friction proper to that tender on 
the same distance. On the Liverpool and Man- 
chester Railway, for ascending the two planes in- 
clined ^ and ^ , assistant engines are used, weigh- 
ing with their tender about 18 tons. The addition 
to make on that account, for friction and gravity, is 
therefore, very nearly, 112 tons one mile in each 
direction ; but as the assistant engines are used only 
for about half the number of the trains, allowance 
will be made for this circumstance by adding only a 
work of 56 tons one mile, for each train conveyed 
along the line. Consequently, observing finally 
that the average weight of the engines is 8 tons, 
and that of the tenders 6 tons, which gives m = 8, 
C = 6, we find that the work done by the engines, 
exclusive of the resistance of the air, in the convey- 



504 CHAPTER XVII. 

ance of a train of M, tons along the whole line, is 
represented by the two following expressions : — 

From Liverp. to Manch. . . . 30*79 M^ -f 262 tons 1 mile ; 
From Manch. to Liverp. . . . 86'89 M, + 348 tons 1 mile. 

It is, however, to be remarked, that the result 
thus obtained only represents the work executed in 
the conveyance of the load, as taken independently 
of the resistance of the air against the train, and of 
divers other resistances which the engines have to 
overcome, such as their own friction, their additional 
friction, the pressure arising from the blast-pipe, &c. 
This result is to be considered, then, only as a rough 
estimate, whereon to ground approximate calcula- 
tions, such as may in general be deemed sufficient in 
practice, but not as an exact and mathematical ex- 
pression of the work executed in the motion of the 
train. The result of this research will nevertheless 
be rendered much more exact, by adding to the 
work done in overcoming the friction and gravity^ 
that done in overcoming the resistance of the air 
against the train at the velocity fixed upon for the 
motion. 

Thus, taking 22*5 miles per hour, as the average 
required velocity on a railway for general transit, 
and 15 carriages, exclusive of the tender, as the 
average load, we find that the resistance of the 
air against the train in motion will be 327 lbs., 
which is equivalent to the traction, on a level 
and at very little velocity, of a weight of 55 tons 



OF INCLINED PLANES. 505 

gross. This traction is to be performed by the 
engine throughout all the length of the portions 
of the railway on which the action of the engine 
is not suspended. Consequentiy, in the case of 
the Liverpool and Manchester Eailway, and at the 
above velocity, the resulting addition, in either 
direction, will be 1543 tons one mile; and thus 
the work done in conveying the load Mj, from 
one end of the line to the other, including the 
resistance of the air at the average velocity of 22*5 
miles per hour, will be 

From liverp. to Manch 30*79 M^ + 1805 tons gross 1 mile 

on a level, at very 
little velocity. 

From Manch. to Liverp 36'89 M^ + 1891 tons gross 1 mile 

on a level, at very 
little velocity. 

The calculation which we have just performed 
would equally apply to every other line, with this 
difference, that if the velocity necessary for the 
conveyance were less than 20 to 25 miles per 
hour, as we took it above for railways of great 
velocity, the action of the engine might be sus- 
pended on descents of less inclination than so^; 
and then, in the calculation of the work done by 
the engine, all the motion performed in descending 
inclinations thus fixed for the limit of the use of 
the engine, must be suppressed. 

As a second example of the preceding calcula- 
tion, we will seek the quantity of work executed 



506 CHAPTER XVII. 

by the engines of the Stockton and Darlington 
Railway, in the conveyance of a train of waggons 
along that line. This research, besides, will be 
needM to us in the Appendix to this work, for 
deducing the expense of carriage on that railway. 

We give, in the annexed Table, the section of the 
portion of that line traversed by the locomotives, 
and the quantity of work done in overcoming the 
gravity. As the speed on that railway is but 8 
miles per hour, and the trains are composed of 
24 waggons, which, with their load, weigh 95 tons 
gross; as the average weight of the engines is 
10*5 tons, and that of their tenders 4*5 tons; 
and as, finally, the friction of the engines, which 
are but little taken care of on that line, may be 
estimated at 30 lbs. per ton instead of 15 lbs., we 
find that the inclination which is sufficient to make 
the trains descend, with the velocity fixed for the 
work, is -g^. Taking account then of this limit, 
to deduct from the total trip the planes traversed 
without the help of the engine, we form the follow- 
ing Table : 



OF INCLINED PLANES. 



507 



Work done in wercoming the ffraviiyy an the Stockton and 
DarKngton Railway {portion traversed by the hcomo- 
tives). 



Section of the railway from 
Bnuaelton to Stockton. 


Work done in oyercoming the 
gravity of 1 ton. 


Distances to be 
traversed. 


Corresponding 
inclination. 


From Bnissdton 
to Stockton. 


From Stockton 
to Brusselton. 


miles. 

•46 

•06 

•92 

1-45 

2-25 

1-25 

101 

1-76 

•20 

1^75 

1-61 

1-64 

•23 

209 

1-25 

•03 

•81 

•05 

•80 

M6 


d. TTT 

d. rh 

d. rhr 
d. yfr 
d. rh 
d. Tir 
d. Tir 
d. rir 
d. -rh 
d-TsVa: 
d. rhr 
d. -air 
d. 7+T 
d-TiVs 

d. Tir 


d. TTTT 

d. xfr 
d iVrj 
d. T*X 


tons 1 mile. 

- -552 

- 069 



-1-591 


-1-071 



- -189 

- ^412 

- -427 


- -120 

- -356 





- 038 

- -189 



tons 1 mile. 
-h 552 
+ ^069 
-f 2^385 
-f 4-474 
H- 1-591 
+ 3-457 
-f 1071 
+ 4-867 
-h -189 
+ -412 
-h -427 
+ 3001 
+ -120 
+ ^356 
H- 1-845 


+ r338 
H- ^038 
-f -189 
-f 4^164 


20^78 


-5014 


+ 30-545 



Consequently, calculating, as we did above, for 
the Liverpool and Manchester Railway, we find that 
on that portion of the railway from Stockton to 
Darlington on which the locomotives run, the con- 
veyance of any load Mj, expressed in tons gross, 
exclusive of tender, requires of the engines, inde- 



508 CHAPTER XVII. 

pendently of the resistance of the air, a quantity of 
work represented, in tons drawn 1 mile on 4 level, 
by the foUowing expressions : 

From Bmsselton to Stockton ... 5' 5 M, — 28 tons gross 1 mfle 

on a level ; 

From Stockton to Bnusdton . . 51*33 M^ +552 tons gnMs 1 mfle 

on a level. 

If it be desired, moreover, to introduce in the 
calculation the resistance of the air against the 
trains, the work done by the engines in drawing 
a train of 24 waggons at the velocity of 8 miles per 
hour, will be 

From Bmsselton to Stockton ... 5* 5 M^ + 70 tons gross 1 mfle 

on a level, at very 
little velocity. 

From Stockton to Bmsselton . . 51*33 M^ +745 tons gross 1 mile 

on a level, at very 
little velocity. 

It is to be remarked, that when, in calculations of 
this kind, there occurs an incline followed by an 
equal contrary incline, and when their inclination 
is not sufficient for the action of the steam to be 
dispensed with during the descent, the computation 
of the definitive work done by the engine in tra- 
versing the two inclines wiU give the same number 
as if the line had been level. It is thence to be 
concluded, that taking, as we have done, the re- 
sistance of the air at its average value on all the 
portions of the trip, the work done in the convey- 
ance of the train on the two inclines will be the 



OF INCLINED PLANES. 509 

same as on a level. But this result arises simply 
from this, that in supposing the resistance of the 
air constant, we make a supposition favourable to 
the case of ascents and descents. In effect, if we 
refer to Sect. ii. of the present chapter, and seek 
the resistance of the air against a train of 56 tons 
gross drawn by a locomotive of 65 cubic feet of 
vaporization, traversing either a level line or a 
system of given ascents and descents, we shall in- 
variably find that the resistance of the air is less on 
the level line, though the average velocity is greater ; 
and this is occasioned by the resistance of the air 
increasing as the square of the velocity. Thus, for 
instance, on two slants inclined x5T5r> the velocities 
of the train will be successively 14"90 and 40*00 
miles per hour, which, for 10 carriages besides 
engine and tender, will produce a resistance of the 
air, first of ll4fts. and afterwards of 817, or at a 
medium 465 fts. ; and on the level portion, at the 
velocity of 25*10 miles per hour, the resistance of 
the air will be only 319 fts. 

We are then finally to conclude, from the divers 
researches relative to ascents and descents, com- 
pared with the same length of road traversed on a 
level : 

That on a system of ascents and descents, the work 
performed by the gravity of the train in descending 
an incline, may compensate the work required from 
the engine by that same gravity in ascending the 
contrary incline ; but that in taking account of all 



510 CHAPTER XVII. 

the drcumstances of the motion, the average velo- 
city of the engine will be reduoed, its average load 
augmented, and the duration of the trip increased ; 
whence will result a loss of time, more wear and 
tear of the engine, and an increased consumption of 
fuel. 



Sect. VTI. Of the means of ascending inclined planes 

on railways. 

From what has just been seen, inclined planes are 
always a great obstacle on railways ; they diminish 
the velocity of the conveyance, and augment the 
average traction of the engine. Besides this, to be 
enabled to ascend them, it is necessary to reduce the 
load of the engines below what they could draw on 
a level ; and we have seen that, with regard to fiiel, 
the engines work to greater advantage inasmuch as 
their load is greater. Finally, the use of the brake 
in descending inclined planes causes rapid destruc- 
tion of the rails. It is therefore very important, in 
establishing a railway, to avoid inclined planes as 
much as possible. 

When, however, incUned planes are unavoidable, 
there are four means of effecting the passage over 
them : 1st, by employing a stationary steam engine, 
which performs the traction of the train by means 
of ropes ; 2nd, by employing an assistant locomotive 
engine, which pushes the train from behind and 
drives it to the summit of the plane ; 3rd, by raising 



OF INCLINED PLANES. 511 

the pressure of the steam in the holler of the engine 
so, as to make it capable of a greater effort, with a 
proportionate diminution of velocity ; and 4th, by 
reducing the load of the engines so as to enable 
them to ascend the planes without additional help. 

Stationary engines always obstruct in some way 
the prompt execution of the work, and they expose 
the trains to accident, if the rope used for the trac- 
tion should happen to break. Assistant engines, 
which want a fire kept up, even in the intervals of 
their work, are an increase of expense to the com- 
panies, and consequently oblige them to raise their 
prices. The augmented pressure in the boiler is 
dangerous to the safety of the engines and the pas- 
sengers. Finally, the diminution of the load is a loss 
to the companies, since more trips are required to 
perform the same work. 

When, therefore, a railway contains indined 
planes, we have only the choice of the inconve- 
niences, and it is only by an attentive examination 
of the circumstances of each particular case, that 
the best mode of traversing them can be decided 
upon. Some general ideas, however, on this sub- 
ject, may be formed beforehand, by considering the 
surplus of traction required by a given inclination. 

1st. On a plane inclined y^o the gravity of 1 ton 
is 22 fts., that is to say, about four times the friction 
proper to the waggons. The resistance opposed to 
the motion becomes then immediately five times as 
much as it was on a level. Besides, the engine 



512 CHAPTER XVII. 

must overcome its own gravity, which, for an engine 
of 12 tons, amounts to 269 fts. ; but as, on the other 
hand, the diminution of the velocity of the train, in 
ascending the incline, immediately produces a reduc- 
tion in the resistance of the air and in that arising 
from the blast^pipe, we will neglect at the same 
time these opposite circumstances. Thus, the train, 
as soon as it reaches the foot of the ascent, offers 
about five times its resistance on a level ; and con- 
sequently, if the engine be supposed to have pre- 
viously drawn its full load on a level, there will 
need five engines to get that load to the top of the 
plane. Now, it is readily conceived that, to prevent 
the expenses from becommg too great, the passage 
of ascents ought in no case to require more than 
one assistant engine. It is evident, besides, that this 
can take place on an inclination of y^, only when 
the load given to the engines is limited to about 
half what they could really draw on a level ; for, 
being once arrived at the foot of the plane, that load 
becoming five times as great, will be 2^ times the 
maximum load of which the engine is capable, and 
consequently an assisting engine somewhat stronger 
than the trip engine will suffice to drive the train 
to the summit of the plane. Thus, we see firstly 
that a plane inclined ^hs ^^^y he traversed by means 
of one assistant engine, provided the load imposed 
on the engines be not greater than about half their 
maximum load. 

2nd. Should the ascent be inclined more than 



OF INCLINED PLANES. 513 

x^i it might still indeed be traversed with a single 
assistant engine; but then it is obvious that the 
load of the engines on a level must be reduced 
below what we have just supposed ; and there would 
no doubt be few cases, at least on railways destined 
to the simultaneous conveyance of goods and pas- 
sengers, on which it would be found advantageous 
to fix the load of the engines below the half of their 
maximum load. We may therefore say generally 
that an inclination of xoir ^iU be nearly the limit of 
ascents on which assistant engines may be employed, 
and that, for greater inclinations, recourse must be 
had to stationary engines. 

3rd. On a plane inclined ^^, the gravity of a 
ton is 7*50 fts., and consequently the total resist- 
ance of the train becomes about double what it 
would be on a level. An engine may then without 
assistance ascend an acclivity of that inclination, 
provided its load on a level do not exceed the half 
of what it might be. We may therefore consider a 
plane of this inclination as being nearly the most 
inclined that can be admitted on a railway without 
being constrained to employ assistant engines. 

Thus, we are led to the following general con- 
clusions : — 

1st. On planes whose inclination does not exceed 
•3^, the traction may be performed without ad- 
ditional help ; 

2nd. On inclinations comprised between y^ and 

2l 



514 CHAPTBR XVII. 



XoiTf it will generally be necessary to have recourse 
to assistant engines ; 

3rd. On planes more inclined than t^* it will 
most commonly be found advantageous to employ 
stationary engines. 

Nevertheless we here repeat that the attentive 
examination of the circumstances of each case, can 
alone fix the choice in a decisive manner, and it is 
only with a view to indicate how that examination 
should be proceeded in, that we have entered into 
the foregoing considerations. 

Sect. VIII. Of the best line for a railway between 

two given points. 

Finally, before terminating this chapter, we have 
still a question to treat of, namely : the choice to 
be made between divers lines, with ascents and 
descents, proposed for a railway to be established 
between two determined points. 

What has been said of the velocity, the duration 
of the trip, and the effective load of the engines, 
on a system of ascents and descents, includes all the 
elements of calculation that the present question re- 
quires ; for, supposing the different plans executed, 
and the projected lines traversed by the same loco- 
motive engine, with the same load, we may imme- 
diately find the average velocity which would take 
place on each, the time of traversing its total length, 
and, lastly, the quantity of work done by the engine 



OF INCLINED PLANES. 515 

in the conveyance of a given load from one ex- 
tremity of the line to the other. This question, 
therefore, offers no remarkable difficulty; but to 
fiidlitate its solution, we think it useful to explain 
more precisely the proceeding to be followed. 

In order to solve the question proposed, the fol- 
lowing way may be used : 

Ist. Since the nature and quantity of the goods 
to be carried are known, the number of trips pei^ 
day will be fixed first of aU, and consequently 
the average load which the engines will have to 
draw. This done, in recurring to the considera- 
tions presented in Chapter XIII., the width of way 
to be adopted will be decided upon, as well as the 
dimensions and weight of the locomotive engines 
to which it may appear advisable to give the pre- 
ference. 

2nd. A Table of the velocity, the time of tra- 
versing 1 mile, and the load on a level, of the 
engine, when passing, with its train, over divers 
planes more or less inclined, will be calculated. 

Afterwards, having the section of the different 
lines proposed, one of them will be adhered to; 
then taking successively each of its inclinations, 
and seeking in the Table the inclination which 
approaches nearest to the one considered, there 
will be found annexed to it the velocity, the time 
of traversing 1 mile, and the corresponding load 
of the engine. Consequently, multiplying the time 
of traversing 1 mile by the length of the plane, we 



516 CHAPTER XVII. 

shall have the time employed in traversing that 
plane; and multiplying the load on a level, by 
the same distance, we shall have the quantity of 
work done by the engine in traversing the plane 
in question. 

Performing therefore the same operation for all 
the different planes which compose the line, taking 
the sum of all the partial times employed to cross 
these planes, and of all the quantities of work ex- 
ecuted by the engine, we shall have the total dura- 
tion of the trip over the line considered, and the 
total work done in the conveyance of the load from 
one end of that line to the other. 

Thus, operating in the same manner for the dif- 
ferent lines proposed, we shall have the total dura- 
tion of the trip over each of them, and the quantity 
of work, in tons drawn 1 mile on a level, done by 
the engines in the conveyance of the determined 
load between the two given points. Afterwards, 
multiplying this last number by the amount of the 
expense of draught per ton per mile on a level, as 
will be indicated in the Appendix, we shall have 
the expense necessary for the traction on the line ; 
adding thereto the other accessory expenses, which 
will likewise hereafter be given, we shall conclude 
the total expense of working the line ; and lastly, 
computing the interest of the capital necessary for 
the execution of each line, and adding it, we shall 
have the total amount of expense corresponding to 
each line proposed. 



OF INCLINED PLANES. 517 

Thus, with regard both to the duration of the trip 
between the two given points and the expenses of 
the work, every means will be afforded of com- 
paring together the different lines projected. 

To show the manner of forming the practical 
Table just mentioned, we will suppose to have been 
adopted a way 5 feet wide, an average load of 50 
tons gross, exclusive of tender, and a locomotive of 
65 cubic feet of vaporization with the dimensions 
indicated in Article III. Chapter XII., excepting the 
pressure in the boiler, which we will suppose 70 fts. 
per square inch. With these the following Tables 
will be formed, and employed as has been indicated 
above. 



518 



CHAPTER XVII. 



M) 



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OF INCLINED PLANES. 



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'|'I'I^-I-I-I-E-I-E'I 



520 CHAPTER XVII. 

In making the requisite comparisons between 
different lines proposed, the above Tables may be 
used, without calculating them again especially for 
eack came. It must only be observed, that the Tables 
are strictly exact for the case of a way 5 feet wide, 
a load of 50 tons, and an engine similar to the engine 
supposed. Consequently, in the question of a rail- 
way on which other loads or other engines are in- 
tended, the comparison by means of these Tables 
must no longer be considered in any other light than 
as an approximation, that may require to be con- 
firmed by an ulterior calculation. In the case then 
wherein such confirmation should seem necessary, 
the calculation must be repeated with more pre- 
cision, taking for each proposed line its true inclina- 
tion, and applying even to each line the width of 
way, the load, and the locomotive likely to give the 
most advantageous results. For those calculations 
we refer to what has been said in the different 
sections of this chapter. 

In the preceding Tables, we have supposed the 
engine to have help, as soon as its velocity, on the 
ascents, should lower to about 1 5 miles per hour ; 
the action of the steam to be suspended, on the 
descents, as soon as the velocity should tend to ex- 
ceed about 30 miles ; and, lastly, the brake to be 
used, to limit the speed to that rate, on all descents 
whereon the trains would of themselves assume too 
rapid a motion. These are, in fact, the limits gene- 
rally adopted on railways at this time. 



CHAPTER XVIII. 

OF CURVES. 

Sect. I. Of the effects of curves on railways. 

Curves in railways present inconveniences which 
are by so much the greater as their degree of curva- 
ture is greater. 

These inconveniences are of three kinds: 1st. 
When a waggon moves in a curve, the wheel which 
follows the outer rail necessarily goes over more 
groimd than that which follows the inner rail. 
Now, in waggons at present in use, the two wheels 
of the same pair are not independent of each other, 
but are fixed invariably on the axle which turns 
with them. Therefore the distance described by 
the one cannot be less than the distance described 
by the other, except the latter be drawn without 
turning over the difference between the two distances 
to be described. This is in consequence an addi- 
tional resistance offered to the motion. 

2nd. The centrifugal force created in the passage 
of the curve, by virtue of the velocity of the motion, 
may urge the waggons outwards, so far as to pro- 
duce a contact and consequently a friction of more 
or less energy of the flange of the wheel against the 



522 CHAPTER XVIII. 

outer rail; and the resistance produced by this 
cause is much more injurious than the former one, 
because the friction takes place on the whole of the 
distance performed by the wheel, and not merely on 
the difference of the distances performed by the two 
wheels. 

3rd. Finally, the centrifugal force of the motion 
may be such as not only to press the flange of the 
outer wheel against the outer rail, but by pushing 
the wheel violently in a direction tangential to the 
curve, it may drive the flange of the wheel over the 
rail, and thus throw the train out of the rails. 

We are about to consider successively these dif- 
ferent effects of curves. 



Sect. II. Of curves the resistance of which is cor- 
rected by the conical inclination of the wheels of the 
waggons. 

The wa^on wheels in use on railways are not of 
a cylindrical form. On railways of about 5 feet 
width of way, they are made of 3 feet in diameter 
at their inner edge, near the flange, and 2 feet 
11 inches at their outer edge. The wheel is ori- 
ginally cylindrical, but the conical inclination is 
produced by the addition of a tire or band of wrought 
iron, which gives to the wheel its definitive diameter, 
and whose thickness on one side is half an inch less 
than on the other. Figure 29 represents the shape 
of this tire on a scale of i of its real size. The 



OF CURVBS. 523 

width of the tire being 3^ inches, its conical inclina- 
tion is ^ inch on 3^ inches, or ^. 

The original object of this form of wheel is to 
prevent a strong side wind, or the accidental de- 
pression of one of the rails, from driving the wag- 
gons on one side of the road, and thereby producing 
a friction of the flange of all the wheels of that side 
against the lateral surface of the rail, that is to say, 
a considerable resistance against the motion. By 
means of the above-mentioned disposition, this 
lateral displacing of the train becomes more dif- 
ficult ; and if nevertheless, from any cause, it do 
take place, and the waggons have been momentarily 
thrown on one side of the railway, the wheels on 
that side immediately increasing in diameter, begin 
to advance quicker than those on the opposite side, 
and consequently bring back the train to its normal 
position between the rails. 

The conical inclination of the wheels suffices, of 
itself, to remedy the inconveniences of the passage 
over curves, when the degree of curvature of the 
latter does not exceed certain limits. In effect, if 
the two rails of the road be supposed exactly level 
one with the other, it is plain that in the passage 
along the curve, the centrifugal force of the motion 
will drive the waggon towards the outer rail. But 
gradually as the waggon is thus laterally displaced, 
the wheel on the outer side turns, by reason of its 
conical form, on a circle of still greater and greater 
diameter, and the inner wheel, on the contrary, 
turns on a diameter still less and less. In this state 



524 CHAPTER XVIII. 

of things, the two wheels of the same pair assume, 
by the fact, different diameters. Moreover, it is the 
outer wheel which acquires the greater diameter, or 
which performs the greatest distance in the same 
time ; consequently the waggon now tends, of itself, 
to turn in the direction of the curve. It will readily 
then be conceived how this disposition of the wheels 
may remedy the inconveniences of certain curves, 
but it will now be proper to particularize still 
further the effects which are then produced. 

The calculation of these effects evidently depends 
on two things : the intensity of the centrifugal force 
produced by the motion of the waggons in the curve, 
and the intensity of the centripetal force produced 
at the same time by the inequality of the wheels of 
the waggons. We shall then, first of all, call to 
mind the value of those two forces. 

The centrifugal force, in the curve whose radius 
of curvature is p, has for its expression, representing 
the velocity of the motion by V, and the mass of the 
moving body by m, 

/=m — ; 
P 

but P being the weight of the same body, and g the 
accelerating force of gravity, we have 

P = 5riw, whence m = -. 

Therefore the centrifugal force has also the value 

P V^ 

J • 9 

9 P 



OF CURVES. 525 

which is the expression of the centrifiigal force for a 
body of a given weight P, set in motion with the 
velocity V, in a curve whose radius of curvature 
is p. 

In this expression, g is the accelerating force of 
gravity, or, as is well known, double the space 
described in the unit of time by a falling body in a 
vacuum. Taking the second as the unit of time, and 
the English foot as the unit of space> we have 
g = 33. Referring then to the same units the 
velocity V and the radius of curvature />, we shall 
have the measure of the centrifugal force expressed 
by its ratio to the weight P, or represented by a 
weight. For instance, if the velocity of the motion 
be 20 miles per hour, or 29*3 feet per second, and 
the radius of curvature be 500 feet, the centrifugal 
force will be 



/ P y ^9*3 1 p 

•' 33X500 19 ' 

that is to say, in this case the centrifugal force will 
be 1^ of the weight of the moving body. 

It clearly appears that, when the velocity of the 
motion and the radius of the curve are known, the 
centrifugal force which urges the body out of the 
curve is easily found. We now pass on to the cen- 
tripetal force produced by the inequality occasioned 
in the wheels of the waggon, by virtue of its lateral 
deviation. 

When two wheels joined invariably together by 



526 CHAPTER XVIII. 

the same axle, roll on unequal circumferences, or, 
in other words, cease to be equal to each other, it 
is clear that instead of together forming a cylinder, 
they form a rolling cone. If ab and cd (fig 30) 
represent the respective diameters of the two wheels, 
and the extremities of those diameters be joined by 
straight lines, these will meet at a certain point o, 
which will be the vertex of the rolling cone formed 
by the two wheels ; and the motion of the waggon 
borne on the two wheels will be the same as that of 
the cone cod. 

But when a cone or frustum of cone is laid flat, 
or along one of its generative lines, on a horizontal 
plane, and it is ui^ed onward by a force applied 
at its centre of gravity, suppose at m, it tends to 
assume a circular motion round its vertex o ; and if 
we wish to prevent it following that curve, and to 
make it move straight forward, the force to be over- 
come will be a force precisely equal, and contrary to 
that which it would be necessary to apply to a body 
directed in a straight line, to curve its direction 
according to the circumference of the circle described 
by the point m round the point o. Now that force 
is the centrifugal force in the circle whose radius is 
om. Denoting then by / the radius of that circle, 
which depends on the difference of diameter of the 
two wheels, and preserving the other notations 
as above, the centripetal force thus created by the 
motion of the cone, will have for its value 

P V» 

— . —7- . 

9 p 



OF CURVES. 527 

Moreover, putting D' and D'' for the respective 
diameters of the two wheels, and e for the width of 
the road, or the space which separates the wheels, 
it is plain, from the figure, that we have the pro- 
portion 

whence we derive 

'^ 2 ' u- jy ' 

But on the other hand, if the tire of the wheel is 
inclined ^, as has been shown above, every inch of 
lateral deviation of the waggon, will produce in the 
wheel a difference of radius of \ inch, or a difference 

of diameter of f inch. More generally, if ~ express 

a 

the inclination of the tire of the wheel, a deviation 

of the waggon expressed by X will produce in the 

wheel a difference of diameter expressed by 

2x 

— ^^ • 

a 

So that if D represent the original diameter of the 
wheel, and D^ its diminished diameter, corresponding 
to the deviation X, we have 

a 

and similarly, the opposite wheel will receive an 
increase of diameter expressed by 



528 CHAPTER XVIII. 

D''-D=— . 

a 

But by adding and subtracting these two equations 
we have 

a 

and 

D''+D = 2D. 

Hence, finally, the centripetal force above, produced 
by a given lateral deviation X, is expressed by 

P.ra 4X 



*V^ 



g aeJy 

Thus, we have the centrifugal force produced in 
the waggon by the fact of its motion in the curve, 
and the centripetal force produced in the same 
waggon by the conical inclination of its wheels. 
But it is to be observed, that the former of these 
forces is constant for a given train, curve, and 
velocity ; whereas the second varies with the lateral 
deviation \ of the waggon. As soon then as the 
waggon enters the curve, the centrifugal force will 
begin to exert its effect; it will drive the train 
towards the outer rail ; a certain deviation X will be 
produced, and, as its consequence, a centripetal force 
which will increase more and more. But since the 
centrifugal force is constant, whereas the centripetal 
force on the contrary is increasing, and as these two 
forces act in contrary directions on the waggon, they 
will quickly settle at a point where they will hold 



OF CURVES. 529 

each other in equilihrium. Then the waggon will 
cease to obey the centrifugal force, and will no 
longer be driven out of the curve. 

The point at which the two forces will be equal is 
given by the equation 

p V» P V^ 



or 



9 


P 


9 


P 


P 

9 


P 


_ P 

9 


ya 4X 
aeD 


P = 


-Py 


or X, = 


aeD 

A 



which gives 



As soon as the lateral deviation of the train shall 
have attained this point, it is clear that the waggons 
will continue their motion without having any ten- 
dency to leave the rails, that is to say, not only 
without risk of being thrown off the road, but even 
without the flange of the wheels being brought into 
contact with the outer rail. Besides, since we have 
at the same time p = py that is to say, since the 
vertex of the fictitious cone, formed by the system 
of the two wheels, will coincide with the centre of 
the curve, it is evident that the waggon will turn 
exactly with that curve without any dragging of one 
of the wheels on the rail. 

Thus, on all curves on which the waggon may be 
sufficiently displaced, the effect of the curve will be 
corrected. But in the construction of railways, it is 
usual to give but half an inch of play to the wag- 
gons, on each side, on the railway ; that is to say, 

2 M 



530 CHAPTER XVIII. 

that during the normal position of the waggon 
between the rails, the beginning of the flange of each 
wheel is ^ inch from each rail. The greatest value 
therefore that can be given to X, without making the 
flange of the wheel rub, is ^ inch, or '0417 foot ; and 
consequently the utmost curve that can be remedied 
by the conical inclination of the wheels, will be 
given by the value of p which corresponds to that 
maximum deviation, in equation 

aeD 

Making then this substitution, and replacing at 
the same time a, e and D by their ordinary values, 

namely, -= y, e = 4*70 feet, and D = 3 feet, we 
a 

have for the least possible radius of curvature, 

p'= 592 feet. 

Consequently, it appears that with the conical in- 
clination adopted, of \ for the tire of the wheel, 
and the play of the waggons ^ inch on the rails on 
each side, there may be constructed on railways 
curves of 600 feet of radius, without the flange of 
the outer wheels of the waggon being exposed to 
touch the rails on that side. As, however, this 
result supposes the two rails exactly level with 
each other, and that there might occur, dining 
the work, an accidental depression of the outer 
rail, wJhich would expose the flange of the wheel 
on that side to rub against the rail, we will, for 
greater security, limit the foregoing result to curves 
having 1000 feet of radius. 



OF CURVES. 531 

It must however be added, that there exists, in 
the passage of curves, a particular cause of re- 
sistance which we have not yet treated of, and 
which subsists notwithstanding the conical inclina- 
tion of the wheels. It consists in this, that the 
two axles of each waggon are parallel to each other, 
whereas for the wheels to turn freely along the 
curve, like the cone to which we have assimilated 
them, the two axles ought to be convergent, on 
the side of the centre of the curve, and ought to 
concur precisely to that point. But as long as the 
question regards only curves of 1000 feet of radius, 
this circumstance may very well be neglected. In 
effect, the width of the way being 5 feet or -5^ of 
the radius of the curve, it is plain that for the axles 
to converge to the centre of the curve, their distance 
apart, on the side of the inner rail, should be ^^ 
less than on the side of the outer rail. Now the 
distance between the axles in their parallel position 
is about 5 feet or 60 inches : the inclination suitable 
to them would then be -yj^j^ of 60 inches or 3-tenths 
of an inch ; and this smaU quantity is to be divided 
into quarters between the four extremities of the 
axles, which would make 7-hundredths of an inch 
at each of these points. But as so very small a 
measure is quite inconsiderable in practice, and 
as, besides, the flexibility of the springs on which the 
axles are mounted easily yields to so slight a devi- 
ation, we deem it perfectly needless to dwell on this 
circumstance. Curves therefore of a radius not less 



532 CHAPTER XVIII. 

than 1000 feet, may without inconvenience be con- 
structed on railways. 

By augmenting the play of the waggons on the 
railway, or the conical inclination of the wheels, 
this faculty might be extended to curves of less 
radius; but as it might be apprehended that the 
result would be a continual rocking of the waggons 
during their motion on the straight parts of the 
railway, we limit our views here to the determining 
of the curvature which is possible in the present 
state of things. 

Sbct. III. Of the superelevation of the outer rail to 
be employed in curves whose curvature is not cor- 
rected by the conical inclination of the wheels. 

From what has just been seen, if a curve had a 
radius of curvature less than 1000 feet, and if 
nothing else were changed in the ordinary disposition 
of the rails, the flange of the outer wheel might come 
in contact with the rail on that side, before the 
proper deviation of the wa^on could oppose a suffi- 
cient counterweight to the centrifugal force which 
produces that motion. The result would be not 
only a friction of the flange against the rail, but a 
possibility of the train itself being thrown off the 
rails. It will therefore be proper to consider what 
are the means of preventing that effect. 

Now it is evident that by giving, throughout the 
curve, a superelevation to the outer rail above the 
inner, we shall make the railway form a plane 



^ 



OF CURVES. 533 

inclined in the direction of its width. The waggons 
placed on this inclined plane must, hy virtue of their 
gravity, slide towards the inner rail, which is the 
lowest. On the other hand, the centrifugal force 
drives them towards the outer rail, which is higher. 
We thereby then create a counterpoise to the centri- 
fugal force. Thus, by this disposition, we are enabled 
to prevent the waggons being thrown off the line. 

But it is to be remarked, that since the waggons 
may always deviate half an inch laterally, without 
the flange of the wheel touching the rail, this de- 
viation must first be taken advantage of to balance 
a portion of the centrifugal force. It is simply 
then the remainder, or the difference between the 
centrifugal force and the centripetal force arising 
from the greatest deviation of the waggons, that 
we need counteract by means of the superelevation 
of the outer rail. 

If we denote by y the superelevation of the outer 
rail above the inner, since e expresses the width of 
the way, the inclined plane on which the waggons 
are placed, during the passage of the curve, will be 

inclined ^; and consequently the gravity of the 

waggons will draw them towards the inner rail with 
the force 

PxL 

e 

Now it is required that this force, joined to the 
centripetal force due to the greatest possible de- 
viation of the waggons on the rails, hold the centri- 



534 CHAPTER XVIII. 

fugal force in equilibrium. Calling then p the radius 
of curvature corresponding to the greatest lateral 
deviation of the waggons, as was found in the pre- 
ceding section, we shall have 

P y .P v«_p v« 

^ 9 P 9 P 
which gives 

9 ^P P^ 

Consequently, substituting for p its value already 
found, p-^ 1000 feet, and at the same time re- 
placing e and g by their corresponding values, 
namely, e = 4*70 feet and ^ = 33 feet, it is plain 
that, for every curve, it will be easy to determine 
the superelevation to be given to the outer rail, to 
counterbalance the centrifugal force, and to displace 
the waggon as much as may be possible, without 
however making the flange of the outer wheel rub 
against the rail. 

It must however be added here, that as the 
necessary superelevation, or the value of y, in- 
creases in the ratio of the square of the velocity 
of the motion, it is indispensable to calculate y, 
not for the average velocity of the motion, but 
for the greatest velocity the trains can acquire. 
Otherwise the superelevation of the rail would no 
longer suffice for cases of very great velocity, and 
accidents might happen in the curves. 

Performing the calculation for difierent velocities, 
and for a railway 5 feet wide, we obtain the follow- 
ing results : 



OF CURVES. 



535 



Table of the superelevation to be given to the outer rail in 

curves. 



Designation of the wsggons 
. and the wmy. 


Radius 
of the 
curre. 


Sap^rderation to he giren to the outer rail, 

in inches, the maximum relodty of the 

motion, in miles per hour, being : 


90 miles. SO miles. 


40 miles. 


50 miles. 


60 miles. 


Waggon with wheels 3 feet 

in diameter. 
Width of way, 4^70 feet 
Play of waggons, on the rail- 

way, on each side, '5 inch. 
Inclination of the tire of the 

wheel, |. 


feet. 

900 
800 
. 700 
600 
500 


inches. 

•16 
•37 
•63 
•98 
1^47 


inches. 

•37 

•83 

1^42 

2-21 

3-31 


inches. 

•65 
1-47 
2^52 
3*92 

ft 


inches. 

102 
2-30 
3-94 

tt 
tt 


inches. 

1-47 
3-31 

ft 

tt 

tt 



When the outer rail of a curve has this super- 
elevation, it is clear that, if a train of waggons 
traverse the curve at the maximum velocity for 
which the superelevation has been calculated, the 
train will deviate laterally as far as the rise of the 
flange of the wheel, and will continue its motion 
in that position to the end of the curve, since the 
divers forces then applied to the waggon, either to 
drive it outwards, or to bring it back within the 
curve, will hold each other in equilibrium. There 
will be no risk of accident then to fear ; but the 
resistance of the train will be greater than on a 
railway in a straight line. In effect, the curve 
traversed will have a radius expressed by p, and 
the rolling cone, formed by the conical inclination 
of the wheels, will have the radius p\ which is 
greater. For the cone to roll of itself along the 
curve, making the wheels describe distances, un- 
equal in the same proportion as the lengths of the 
outer and inner rails, it would be necessary, as has 



536 CHAPTER XVIII. 

been seen above, that p should be equal to p. The 
dragging of the wheels will therefore take place on 
the difference between the circumferences described 
with the radii p and p. The parallelism of the 
axles, besides, will have an effect by so much the 
greater as the radius of the curve is smaller. The 
superelevation of the rail, such as we have deter- 
mined it above, is then to be considered as rendering 
impossible, in the regular state of things, that the 
train should be thrown off the rails, and not as 
destroying all increase of resistance in the passage 
of curves. Some ingenious means have been pro- 
posed to attain this latter result, but as they are not 
yet sufficiently confirmed by experience, we refer 
the reader to the publications in which their in- 
ventors have developed the advantages to be de- 
rived from them. 

We will however observe that, in general, the 
only object of all the modes proposed for passing 
curves, is to obviate the inconveniences which they 
offer in the normal state of things. But a rail 
broken or accidentally raised, a stone fallen on the 
road, an axle or a wheel broken, always present 
chances of much more serious accidents on curves 
than on the straight Une. 



APPENDIX. 



EXPENSES OF HAULAGE BY LOCOMOTIVE ENGINES 

ON RAILWAYS. 

To complete the knowledge of locomotive engines, it still 
remains to consider them with regard to their economy ; 
that is to say, to examine the amount of the expenses 
attending the haidage by means of locomotive engines 
on railways. This research will be the object of the 
present Appendix. 

We shall draw the documents we have to present on 
that subject from the two most ancient enterprises of the 
kind in England : the Liverpool and Manchester, and the 
Stockton and Darlington Railways. They will have, be- 
sides, the advantage of presenting examples of two very 
different sorts of conveyance: the one rapid, and prin- 
cipally composed of passengers; the other slow, and 
consisting of goods. 

We shall divide the expenses incident to locomotive 
engines on railways in the following manner : 

The repairing and maintaining of the 'engines, their 
consumption of fuel, and the expenses for conducting 
them, constituting together the expenses for locomotive 
power, properly so called ; 

The expenses for the maintenance of the way; 

The office expenses and contingencies, which, united 

2n 



538 APPENDIX. 

with the preceding, give the total expense of the haulage 
by means of locomotive engines on railways ; 

Finally, we shall conclude with a glance at the receipts 
compared with the expenses, which will show the profits 
arising from these enterprises, to the companies who 
carry them into execution. 

In treating of these various subjects, througliout this 
Appendix, we shall ^ve the amount of expenses per ton 
gross, that is, including the weight of the waggon which 
conveys the goods. This is the most accurate method, 
since it refers to the effort really exerted by the engines, 
and to the weight effectively borne by the rails; and it 
matters little, as regards the engine or the rails^ whether 
in this total weight, a half merely or any other proportion 
be composed of merchandise or useful weight. It will 
afterwards be easy, on any line of road, to deduce the 
cost of conveyance per ton 0/ goods, when once, on that 
line, knowledge is obtained of the weight of the waggon 
compared with that of the load. In the weight of a 
loaded waggon, generally, the load is two-thirds, the 
waggon one-third, which establishes at |- the ratio of the 
effective tons, or tons of useful weight, to the tons gross. 



Sect. I. Ejcpense /or repairs 0/ locomotive engines. 

Among the expenses just enumerated, that which will 
naturally first engage our attention is the expense for 
keeping the engines in repair. 

Before we enter into any calculations on tiiat head, it is 
necessary to mention that what is meant by repairs to the 
engines, is nothing less than their complete re-construc- 
tion; that is to say, when an engine goes into repair, 
unless it be for some trifling accident, it is taken to pieces 
and a new one is constructed, which receives the same 
name as the first, and in the construction of which are 



EXPENSE FOR REPAIRS OF ENGINES. 539 

made to serve all such parts of the old engine as are still 
capable of being used with advantage. The consequence 
of this is^ that a re-constructed or repaired engine is 
literally a new one. The repairs amount thus to con- 
siderable sums^ but they include to a great extent the 
renewal of the engines. 

According to the Tables at the end of this work^ it will 

' be seen that in the year ending on the 30th of June, 1834^ 

the repairs of the engines of the Liverpool Railway cost — 

From June 30, to December 31, 1833. 

Materials for repairs .... £ 3.755 3 7 

Workmen 4,401 4 10 

Repairs out of the establishment 613 3 9 

£8,769 12 2 

From December 31, 1833, to June 30, 1834. 

Materials £4,140 19 6 

Workmen 5,-432 8 8 

: 9.573 8 2 

£18,343 4 

The question is now what was the work executed by 
those engines during that interval ? Now, referring to the 
same Tables which will be found below, it will be seen 
that the goods conveyed on the line during the year 
were — 

Between Liverpool and Manchester 139,328 1. 

On part of the hne, making an average of 15 miles,^ 

24,934 1., which, on the whole, is equal to . . . 12,467 

Total . . . 151,795 1. 

In the Tables just mentioned, there appears indeed 
some other haulage executed, such as goods for Bolton 

^ The distance to which the Company carries the Wigan and 
Warrington goods, which form the principal part of this article, is 
15 miles. 



540 APPENDIX. 

and coal for several places along the line ; but this work 

is done by engines which do not belong to the Company^ 

so that their repairs are not included in the following 

reports^ and for that reason we do not take it into account 

in this place. 

The above weight is that of the goods conveyed^ to 

which must be added the weight of the waggons. Now, on 

that railway, the average load carried on a waggon is 3*5 1., 

and the waggon itself weighs 1*5 t. ; so the weight of the 

carriages that served for the above-mentioned tonnage will 

be known by multiplying the number obtained^ by the 

1*5 . r 

ratio ---. And as, moreover, the engines, for want of 

suf&cient returning traffic, are obliged to. bring back half 
the waggons empty in one of the two directions, or i of 
the whole, we shall have for the gross weight drawn by the 
engines in the course of the year — 

Weight of the goods 151,795 1. 

Weight of the corresponding waggons .... 65,055 
Weight of the waggons brought back empty . . 1 6,264 

233,1 14 1. 

This is the tonnage of the goods, to which must be 
added that of the travellers. In the course of the year, 
415,747 travellers were conveyed from one city to the 
other in 6570 trips.* This makes an average of 64 
travellers per train. The coaches required for that num- 
ber of travellers, including the empty carriages added to 
each train to-be ready for any emergency, are six carriages 
of the first class, or five of the second.' 

' Tliia is the number of the travellers inscribed in the Com- 
pany's books. It includes neither the travellers put down nor 
those taken up on the road, the numbers of which balance each 
other. 

' The first-class carriages are glass coaches, containing each 13 



EXPENSE FOR REPAIRS OF ENGINES. 541 

The weight of six first-daas coaches, indading the mail, is 21 t. 
The weight of a second-class train of five carriages, in- 
dading one glass coach, is 12*6 

Lastly, for 13 trains of the first class there are 16 of 
the second. Thus, the average weight of the carriages for 
every 64 travellers may be reckoned at 16*4 1. 

Consequently, the gross weight corresponding to the 
travellers conveyed was — 

415,747 travellers, at 15 per t 27,717 1. 

Corresponding weight of the carriages .... 107,748 
Luggage of the travellers, at 28 lbs. each . . . 5,197 

140,662 1. 

Thus the total weight drawn during the year, by the 
engines belonging to the Company, was — 

Gross weight for goods 233,1 14 1. 

Gross weight for travellers 140,662 

373,776 1. 

Now we have already shown in this work (Chap. XVII. 
Sect. VI.) that, taking into account the siirplus of resistance 
caused by the gravity of the train and the engines, on 
the different inclines of the Liverpool and Manchester 
Railway, the quantity of work executed in the traction of 
any load, over the whole extent of the line, may easily be 
determined by the following expressions : 

From Liverpool to Manchester . . W. = 30*79 M, 4- 262, 
From Manchester to Liverpool . .*W. = 36*89 M, + 348, 

in which W figures for the quantity of work executed, 
expressed in tons groiA drawn one mile on a levels M , the 

persons ; they weigh 3*65 1. Those of the second dass are open, 
and have 24 places; their weight is 2*23 1. Lastly, the mail- 
coaches weigh 2*71 1., and carry 10 travellers. Each glass coach 
has besides one outside place. 



542 APPENDIX. 

load of the engine, in tons gross estdmmm oftemdery and 
the numbers 262 and 348 the average woik canaed by the 
gravity of the engines and their tender, and by the traction 
of that tender. Taking dien a mean between these two 
expresnons, it will appear that the oonTeyanoe of a load 
M, finom one end erf the line to the other, in both direc- 
tions, will produce a q[iiantity of woik expressed by 

W.=3d-84M. +305 tons gross 1 mile on a levd« 

This premised, as the above 373,77^ tons gross were 
conveyed by the engines in 11,656 trips, it follows that 
die average load of the engines per trip was 32 tons gross. 
Substitnting then this number for M, in the preceding 
expression^ we find duit the work done by the engines in 
each trip was 1387*9 tons gross drawn 1 mile an a ieveL 
Thns as the engines performed in aD 11,656 trips, the total 
work done by them was 

11656x1387*9= 16,177,080 tons gross drawn 1 mile on a level; 

and the ratio of this number to the real conveyance 
effected, namely, 373,776 tons gross drawn 29*5 miles, 
or 11^026,392 tons gross drawn 1 mile, shows at the same 
time that, on that line, the gravity and draught of the 
tendera increase the work of tiie engines in the |Hroportion 
of 1-467 to 1. 

For the work above stated, the repaira of the engines 
cost £ 18,343 0». 4d. This smn, reduced to pence, gives 
4,402,324 d. Consequently the repaira, per ton.gross con- 
veyed 1 mile on a level, amounted to 

4402324^ 



15177080 



=•272^. 



To perform this work, tiie engines made 6570 trips 
with travellers, that is to say, at a velocity of 20 miles per 
hour; and 5086 trips, with goods, or at a velocity of 12-5 
miles an hour. The average velocity of the haulage was 
therefore 16*73 miles per hour. 



EXPENSE FOR REPAIRS OF ENGINES. 543 

We have said elsewhere that, at the time of these ob- 
servations, the Liverpool and Manchester Railway Com- 
pany possessed thirty locomotive engines. It must not 
be concluded, however, that that number is necessary in 
order to perform the above-mentioned haulage. Of these 
30 engines, about one-third were useless. This third 
consisted of the most ancient which, having been con- 
structed at. the first establishment of the railway, at a 
time when the Company had not yet obtained sufficient 
experience in that respect, are found now to be out of 
proportion with the work required of them. The engines 
in daily activity on the road "amounted to about 10 or 11, 
and with an equal number in repair or in reserve, the 
business might have been completely ensured; for the 
surplus, above that number, was nearly abandoned. 

We shall complete what has just been smd on the 
Liverpool and Manchester locomotive engines, by adding 
a document that will show what these engines are capable 
of executing in a daily work, and the improvement they 
have undergone in the course of the last few years, with 
respect to their construction. 



544 



APPENDIX. 



Work done by the ten best locomotive engines of the lAver- 
pool and Manchester Railway, during the years 1831, 
1832^ 1833^ and the first twelve weeks 0^1834. 



Year. 



Name of the engine. 



Total time 

the engine 

has been on 

the road, 

either in 

activity or 

in repair. 



Total 
travelled by 
the engine. 



1831. 



Mkrcurt 

JUPITBR 

Planbt 

Saturn 

Mars 

Majbstic 

North Star .... 
Northumbrian . . . 

Phcbnix 

Sun 

Total 

Ayerage per week 



Weeks. 
52 
44 
52 
38 
50 
52 
52 
52 
52 
37 



481 



Blika. 
23,212 
22.528 
20,404 
19,510 
18,645 
18,253 
15,677 
15,607 
15,405 
13,434 



182,675 
380 



1832. 



Vulcan 

LiVBR 

Vbnus 

Etna 

Saturn 

Vbsta 

Victory 

Planbt 

Sun 

Fury 

Total 

Average per week 



52 
43 
52 
52 
52 
52 
52 
52 
52 
52 



511 



26,053 
22,651 
20,464 
20.399 
20,312 
17.739 
17,082 
16,885 
16,5«5 
15.603 



193,723 
379 



EXPENSE* FOR REPAIRS OF ENGINES. 



545 



Work done by the ten best locomotive engines of the lAver^ 
pool and Manchester Railway, during the years 1831^ 
1832^ 1833^ and the first twelve weeks of 1834. 



Year. 



1833. 



Name of the engine. 



JUPITBR 

Ajax 

FiRBPLT 

LiVBR 

Pluto 

Vesta 

Lbbds 

Saturn 

Vbnus 

Etna 

Total 

Average per week . . 



Total time 

the engine 

has heen on 

the road, 

either in 

activity or 

in repair. 



Weeks. 
52 
52 
39 
52 
52 
52 
48 
52 
52 
52 



503 



Total distance 
travelled hy 
the engine. 



Miles. 

31,582 

26,163 

24,879 

23,134 

20,308 

19,838 

19,364 

18,738 

18.348 

17,763 



220,117 
438 



1834. 



FlRBVLT 

Vulcan 

Saturn 

Liter 

Sun 

Etna 

Leeds 

Ajax \ 

Venus 

Pluto 

Total 

Average per week 



12 
12 
12 
12 
12 
12 
12 
12 
12 
12 



120 



8,542 
8,526 
7,290 
7,080 
7.080 
6,557 
5,712 
4,890 
4,632 
4,246 



64,555 
538 



546 APPENDIX. 

As we have already said that the average load of the 
engines, on this railway, is 32 tons gross^ exclusive of 
tender y it would be easy to deduce firom this Table, the 
number of tons gross which have been carried 1 mile by 
each of the engines during the time of its work. Similarly, 
by dividing the number of miles travelled by the length 
of the railway, which is 29*5 miles, we might dedace firsts 
the number of trips performed by each engine ; and then, 
recollecting that each trip, with the average load of 32 
tons gross, corresponds to 1388 tons gross drawn 1 mpe 
on a level (page 542), we might deduce the number of 
tons gross drawn 1 mile on a level by the engine, either 
in the course of a year, or during the whole time it was 
on the line. We will not offer this calculation for each 
engine, but will ^ve the result of it for those two^ among 
them, which have done the most work. 

At the time of the completion of the above Table^ the 
Liver had been employed on the railway during 107 
weeks, had travelled a distance of 52,865 miles, or drawn 
2,487^140 tons gross, tender included, one mile on a level; 
the Firefly had worked 57 weeks, had travelled a distance 
of 33,421 miles, or drawn 1,572,360 tons, gross, tender 
included, one mile on a level; the average velocity at 
which these loads had been, drawn was 16*73 miles per 
hour, and neither of these engines, at the period in 
question, had yet required a thorough repair.^ 



To give an example of the expense of repairs of lo- 
comotive engines, under other circumstances, and with 
engines of another construction, we will here set down 
the work performed by the locomotive engines on the 

K 

^ The greater part of these excellent engines were built by 
Mr. R. Stephenson. The Liver engine is the work of Mr. Edward 
Bury, of Liverpool. 



EXPENSE FOR REPAIRS OF ENGINES. 547 

Stockton and Darlington Railway, during the same year, 
that is to say, from Jmie SO, 1833, to June SO, 1834, and 
the amount of expenses for repairing those engines during 
the same space of time. 

On this railway, the engines performed, in the course 
of the year, and descending with their loads, a number of 
trips which, estimated in trips of 20 miles each, according 
to the custom of the Company, amounts to 5318*5, or 
5119 trips^of 20*78 miles each; and this necessarily 
carries with it an equal number of trips in ascending 
with the empty waggons. The load of the engines at 
each trip going down, is 24 waggons, carrying 63*6 tons 
effective of coal, and weighing in tons gross 94*8 tons. 
In bringing the 24 empty waggons up again, the load of 
the engines is 31*2 tons gross. Recurring to the expres- 
sion which we have given Sect. vi. Chapter XYII., of 
the work done in conveying a given load on the whole 
extent of this railway, it will readily be perceived that, 
considering the bringing back of the waggons empty, 
every trip descending corresponds to the draught of 2650 
tons gross 1 mile on a level; and consequently the total 
work exiecuted in the year on this railway, amounts to 

13,565,350 tons gross, one mile on a level. 

With regard to the corresponding expenses, it is to be 
noted that, after having for a long while kept and re- 
paired their engines themselves, the Directors of the 
Stockton and Darlington Company decided, in order to 
avoid minute accoimtd, to do all that work by contract ; 
and, in consequence, in 1833, they put their engines into 
the hands of three persons. By the contract entered 
into, the Company paid ^V of a penny per ton of goods 
carried one mile; and, for that price, the contractors 
undertook, not only to keep the engines in good repair, 
furnishing workmen and materials, but also to pay all the 
current expenses of haulage, such as salary of the engine- 



548 APPENDIX. 

men^ fuel^ oil, grease, &c.; and to pay moreover to the 
Company an interest of five per cent, on the capital 
representing the value of the engines, and of all die 
establishments placed at the contractors' disposal for their 
work. 

The total sum paid to the contractors by the Company 
for that object during the year ending June 30, 1834^ 
was 

£11,347 Is. 9<^.; 

and deducting the expenses for rent, interest of capital 
and haulage, the amount of which is known, the Directors 
of the Company reckon that the definitive sum remaining 
with the contractors for the repairs of the engines (bars 
of fire-box included), amount, with the general profit on 
the whole bargain, to 

£5,732 18«. 5d. 

This sum, reduced to pence, gives 

1, 375,901 e^. 

It was expended for the carriage of 13,565,350 tons gross 
one mile on a level ; so that finally the expense, per ton 
gross carried one mile on a level, including the profits on 
the bargain, amount to 

OlOlrf. , 

As a complement to what we have said, and to show, 
on this railway as well as upon the Liverpool one, the 
work the engines are able to perform, we shall, give a 
Table of the haulage executed, and repairs done to the 
engines, during five months of the year 1833. 

To form, in this Table, the column which contain^ the 
work done, in tons gross carried 1 mile on a level, tender 
included, the number of tons of coal carried 1 mile 
descending is multiplied by 2; because, from the cal- 
culation indicated page 547^ the conveyance of a load of 
63*6 tons of coke, along the whole line, or the distance of 



EXPENSE FOR REPAIRS OF ENGINES. 549 

20*78 miles, corresponds, including the return of the 
empty waggons, the gravity, &c., to a quantity of work 
expressed by 2650 tons gross drawn 1 mile on a level; 
and that this number is double the product 63*6 x 20* 7B 
= 1322, which represents the useful work done at each 
trip, or the number of tons of coal carried 1 mile by 
the engine. 

The last column but one of the Table contains the 
amount of expenses for keeping each engine in repair 
during the time it was on the line, and the last column 
contains the same expenses divided per ton gross drawn 
1 mile on a level; but we must add that, at the time 
when this Table was formed, there were, among the 
engines of the railway, twelve completely new. Besides, 
the amount of repairs here set down includes only the 
workmen^s wages, and not the materials, those materials 
having been purchased largely and kept in store. It is 
therefore subjected to these restrictions, that we present 
the foUowing Table. 

Most of the engines of the Stockton and Darlington 
Railway were built by Mr. T. Hackworth, of Brusselton, 
near Darlington. 



550 



APPENDIX. 



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EXPENSE OF FUEL. 551 

Sect. II. Ewpenae of Fuel. 

We have already, in Chapter IX. of this work, related 
experiments from which may be deduced the consumption 
of fuel according to the load the engines have to draw. 
However, as in the intervals of the trips, the fire must be 
kept up, and as, besides, there are always imavoidable 
losses during the work, an increase of expense in that 
respect must naturally be expected in practice. This we 
also learn in a positive manner by the examination of 
facts. 

According to the half-yearly reports of the Liverpool 
Railway Company, for the year ending June 30, 1834, 
the expense for fuel for the locomotive engines was 

£6,079 15«. Se^. 

The number of trips performed was 11,656: conse- 
quently the expense for fuel for each journey amounted to 
10*432^.; and as the average price of coke used during 
that year on the railway was 23*5^., the consumption of 
fuel, measured in weight, amounted to 994*37 ffis. per 
trip. Now we have already seen that the average load of 
the engines, during the year, was 32 tons gross. A load 
of 32 tons, not including the tender, consequently re- 
quired, by the fact, a consumption of coke of 994lbs. 
Thus, as the work corresponding to the conveyance of 
that load from one end of the line to the other is equi- 
valent to 1388 tons gross carried 1 mile on a level (page 
542), it is plain that the consumption of fuel amounted to 

'7161b. of coke per ton gross carried 1 mile on a level ; 

and from the price of coke on that line, that consiunption 
cost 

'090<f. per ton- gross carried 1 mile on a level. 

Our special Experiments given Chapter XL. only give 
an average consimiption of 784lbs. of coke for a load of 



552 APPENDIX. 

32 tona» By this it will be seen that, in practice^ and 
with the nature of the business on that line, the different 
losses amount to one-fourth of the expense of the active 
work. This considerable increase is owing not only to 
the necessary expense for lighting the fire every morning, 
bat also to the necessity, on that Une, of keeping, for the 
passage of the inclined planes, helping engines, the fixe of 
which must remain alight the whole day, although they 
only serve at distant intervals; to the number of trips 
which the engines make almost without load ; and in fine, 
to the long delays between one journey and another. 
These circumstances, that of the helping engines alone 
excepted, are inevitable in a business of the nature of 
that of the Liverpool and Manchester Railway* 

On the Stockton and Darlington Railway the same 
causes of loss do not exist, at least not to the same 
d^ree. 

According to the notes, carefully kept by the Directors 
of that Company to serve as a foundation to the contracts 
they sign, the quantity of coal consumed on an average, 
during one journey of an engine, that ia to say, to convey 
24 loaded waggons a distance of 20 miles down lull, and 
bring them back again empty to the same distance up 
hill^ costs the engine-men 4«. 9}i/., when the coals are at 
5s. per ton. So the weight of coals consumed is 21571bs. 

Now we have seen that the work done in one trip is 
equivalent to 2650 tons gross drawn 1 mile on a level; 
the consmnption of coal per ton gross carried 1 mile on a 
level is therefore 

•814ft.. 

or, from the price of the fuel, 

•0218J. 

This is. nearly the same consumption in weight as. on 
the Liverpool and Manchester Railway. The result may 



EXPENSE OF LOCOMOTIVE POWER. 553 

appear surprising ; for the boilers of the Darlington engines 
are generally constructed on a less economical principle, 
as to the application of heat, than the Liverpool ones ; but 
considering the work of each line, this circumstance will 
easily be accounted for. On the Darlington Railway the 
engines never go off but with a full load ; that is to say, 
that, taking the two trips together, the descending and the 
ascending, the engines draw, as has been shown, an 
average load of 63 tons gross per trip, which circum- 
stance we know to be favourable to the expenditure of 
fuel. If these engines drew only an average load of 32 
tons, like the Liverpool ones, their relative consumption 
would certainly be greater. To this must also be added 
that, on the Darlington Railway, the engines suffer no 
delay between their trips. 

It is to these combined circumstances that the practical 
result appearing in this case must be attributed. As 
railways for goods are generally found to have these 
advantages over railways for travellers ; that is to say, as 
less frequent departures admit of starting the engines 
more completely loaded and with less loss of time between 
the trips, it ought to be consiidered that the comparative 
saving of fuel which we notice, originates in the very 
nature of the work itself. 



Sect. III. Eoepense of locomotive power. 

To the expenses just noted, ilamely, the repairs of the 
engines and the fuel, are to be joined several accessory 
charges for the conducting of the engines, such as engine- 
men^s and assistants' wages, oil,. grease, hemp, &c. The 
amount of these divers objects taken in their detail, is 
reported in the Tables of receipts and expenses of the 
Liverpool and Manchester Railway, which will be given 

2 o 



554 APPENDIX. 

farther on ; but it is necessary to consider them here taken 
collectively. 

These charges, together with the expenses for repairs 
of the engines and the expenses for fuel, constitute the 
expenses of locomotive power, properly so called. It is 
then indispensable to include them in the calculation, in 
order to know the definitive cost of locomotive engines 
used as a means of conveyance. 

It will be seen in the Tables of detail given farther on, 
that on the Liverpool and Manchester Railway the ex- 
penses of locomotive power amounted, during the year 
under consideration, to the sum of 

£29,607 53. lid. 

As we have seen that the work done by the engines 
amounted to 16,1779080 tons gross, drawn one mile 
(page 542), it follows that the expenses for locomotive 
power, were 

'4S9d» per ton gross per mile on a level, at an average velocity 

of 16*73 miles per hour. 

On the Stockton and Darlington Railway, we have said 
that the Company passed a contract for the locomotive 
power, and that the total price paid to the contractors 
during the year was 

£11,347 U. 9d. 

Out of this sum the contractors pay to the Company, for 

rent of work-shops, and interest of capital vested in 

engines, 

£824. 

There remains, then, definitively paid for locomotive 

power, 

£10,523 Is, 9d.i 

and as this sum has defrayed the conveyance of 13,565,350 
tons gross to 1 mUe (page 547), the rate of that expense was 



EXPENSE FOR MAINTENANCE OF WAY. 555 

'186 if. per ton gross per mile on a level, at the speed of 8 miles 

per hour. 

This expense^ however^ refers to coal used as fuel. As 
this circumstance does not occur on the railways recently 
formed^ and particularly on the Liverpool and Manchester 
Railway^ it will be necessary^ in order to have prices com- 
parable between them^ to take into account the difference 
of price of the two fuels. 

Now, the Darlington Company bum •814115. of coal 
per ton gross per mile on a level. Supposing in the two 
kinds of fuel an equal power of producing heat, the con- 
sumption of coke would also be *8141l3., and taking that 
fuel at the Liverpool price, namely, at 23s. Gd. per ton, 
the expense per ton gross conveyed one mile would be 
'I02d., instead of *022«f., which it actually is. There 
would then be an augmentation of expense per ton gross, 
per mile, of 

OSOd, 

Thus, with the use of coke instead of coal on the 
Stockton and Darlington Railway, the expense for loco- 
motive power would amount in this year to 

'2S6d. per ton gross per mile on a level, at the average velocity 

of 8 miles per hour. 

It will be remarked that this expense, compared with 
that of the Liverpool and Manchester Railway, for the 
same object, is within a very little in proportion to the 
velocity on each line, namely, 8 miles per hour in one 
case, and about 17 miles per hour in the other: this is a 
point which we shall again touch upon farther on. 



Sect. IV. Expense for maintenance of way. 

The expenses for keeping the Liverpool and Man- 
chester Railway in repair, during the year under con- 



556 APPENDIX. 

sideration^ from June 30^ 1833^ to June 30, 1834, were^ 
according to the Tables of detail given hereafter, 

£15,776 128. Id. 

During the same time the following weights passed on 
the railway, drawn either by the Company's engines, or 
by engines belonging to other companies, namely : 

OoodB on the whole road 139,328 /. 

on half the road 24,934 tons, making on the 

whole road 12,467 

between Bolton, and Manchester or Liver- 
pool, 38,341 tons, or on the whole road . . 19,170 

Coal on half the line 86,173 tons, or on the whole . 43,086 

1*6 
Conresponding waggoni, 1- of the weight of the goods 128,431 

3*5 
Waggons brought back empty, J^ of the whole • 32,108 

Total for goods and coal 374,590 t. 

Coaches, trayellers, and luggage, as above . 140,662 

515,252 t. 

Thus 515,252 tons gross passed over every mile of the 
railway, exclusive of the weight of the engines and their 
tender. The expenses for maintenance of way having 
been j£ 15,776 12^. Id. for 31 miles, the whole length of 
the railway, or j£508 ISs. Sd, per mile, they amount to 

*237<f. per ton gross per mile. 



On the Stockton and Darlington Railway, during the 

same year, the expenditure for repairs of the road was as 

follows : 

£ 8. d. 

Workmen's wages for repairs to the railway . . 5,320 5 

Materials for ditto 2,578 3 8 

Repairs to bridges 69 17 7 

Repairs to walls and fences 280 7 11 

Contingendes 467 3 7 

8,715 17 9 



i 



EXPENSE FOR MAINTENANCE OF WAY. 557 

And deducting the chaises relative to walls and fences^ 
which are not included in the preceding article for the 
Liverpool and Manchester Railway, as may be seen in the 
detailed accounts presented further on, the amount of this 
expenditure reduces itself to 

£8,435 98. \0d. 

On the other hand, the weights which passed on the 
railway, drawn either by locomotives or by the stationary 
engines or by horses, wei'e : 

ton* to 1 mile. 
375,320 tons of coal, equal in tons carried one mile, to 8,526,904 t.^ 

32,996 tons of Ume-stone 133,064 18,858,193 

17,387 tons of goods 198,225 J 

6,499 tons in passengers, equal to 53,733 

1*30 
Waggons, of the weight of the goods conveyed . 4,345,529 

2*65 

Waggons brought back empty, same weight 4,345,529 

Weight of coaches, in tons carried one mile 161,199 

Total 17,764,183/. 

The expense per ton gross per mile, exclusive of the 
weight of engine and tender, amounts then to 

*1 14(/. per ton gross per mile. 

Taking the repairs of walls and fences into the account, 
this article would give *118i/. per ton gross per mile. 

It must be observed that this expense, as well as that 
above mentioned for the Liverpool and Manchester Rail- 
way, is rather higher than it will be on an average for the 
years to come, on account of an extraordinary replacing of 
the rails of both lines, by other rails of much greater 
strength. 

The expenses for keeping in repair the Stockton and 
Darlington Railway would unquestionably be less, if the 
waggons used on that line were on springs, like those of 
the Liverpool and Manchester Railway. In the present 
state of things, however, those expenses scarcely amount 
to half the expenditure of the Liverpool and Manchester 



558 APPENDIX. 

Railway for the same object ; that is to say^ they are, as 
well as the expenses for locomotive power, very nearly in 
proportion to the velocity on each line. 

It must not however be thought that the great differ- 
ence observed in this respect between the two railways^ 
is exclusively owing to the velocity of the motion. That 
velocity, indeed, constitutes much of it, but the conditions 
attending each sort of business have a no less consider- 
able influence. What we mean is, that the conveyance 
of passengers forming the chief business on iixe Liverpool 
and Manchester Railway, their safety requires that much 
more care be taken of the engines than when the load is 
composed only of coal, as on the Stockton and Darlington 
Railway. The consequence is, that the Liverpool engines 
are kept with a degree of care, we might even say of 
luxury, to which the Darlington ones can by no means 
be compared. To explain our idea completely, we may 
say that the business of the Darlington Railway is a 
business of waggonage, and that of the Liverpool Railway 
a business of stage coaches. 

The data laid down above must therefore be taken each 
in their speciality, that is to say, the one as suitable to a 
slow motion, with engines of a certain construction and 
intended for the draught of goods, and the other to a 
rapid motion with engines of a different construction, and 
intended for the draught of passengers, for which the 
former would be unfit. 

Before we close this article, we must remark that the 
repairs of the railway consist principally in replacing the 
blocks, chairs, keys, and pins. The rails themselves, being 
of malleable iron, seldom break. As for their gradual 
decrease of weight, by wear, that is a very inconsiderable 
effect, as may be seen by the following fact. 

On May 10th, 1831, on the Liverpool and Manchester 
Railway, a malleable iron rail, 15 feet long, carefully 
cleaned, weighed I7711^s. 10^ oz. On February 10th, 1833, 



TOTAL EXPBNSB OF HAULAGE. 559 

the same rail, taken up by Mr. J« Locke, then resident 
engineer on the line, and well cleaned as before, weighed 
176113s. 8 oz. It had consequently lost in 21 months a 
weight of 18^ oz. The number of tons gross that had 
passed on the rail during that time was estimated at 
600,000. Thus we see that with so considerable a tonnage, 
and with the velocity of the motion on that railway, the 
annual loss of the rail was only -^-f^ of its primitive 
weight. So that it would require more than a hundred 
years to reduce it to the half of its present strength* 



Sect. V. Total expense of haulage. 

So far we have seen to what rate per mile the expenses 
amoimt for locomotive power and for maintenance of 
road. But to determine the definitive rate of the expenses 
of all kinds, necessary for working raUways by means of 
locomotive engines, it still remains to make the same cal- 
culation for each of the other expenses incident to these 
engines on the railway. 

Taking each of these charges from the detailed Tables of 
the Liverpool and Manchester Railway Company, and 
dividing it according to the respective work to which each 
refers, we arrive at the following result : — 



r 



560 



APPENDIX. 



Partition of the expenses of haulage on the Liverpool and 

Manchester Railway. 

Expense per ton 
gross per mile. 



£, 8, d, 
15,971 13 6 



25.270 7 1 



10,686 


10 


4 


29,607 


5 


11 


15,776 


12 


1 


2,294 


6 


8 



3,462 15 5 



13,373 6 8 



116,442 17 8 



TnTellen. 



ft 



u 



Repairs to coaches, compeiisation for lug- 
gage lost, offices for booking passen- 
gers ; to be divided according to a gross 
tonnage, for travellers, of 140,662 tons 
(page 541) and for a length of road of 
30 miles, makes '90837^ 

Loading of goods, compensation for ditto, 
cartage in the towns of Liverpool and 
Manchester, loading and miloading of 
coals; to be divided according to 
374,590 tons gross of goods and coals 
(page 556) and for 31 miles of road, 
makes 

Interest on borrowed capital 

Locomotive power already divided (on 
the level) -43925 

Maintenance of way already divided .... '23705 

Stationary engine and tunnels ; to be di- 
vided according to 515,252 tons gross 
(page 556) and for 31 miles, makes per 
ton gross per mile '03447 

Repairs to waggons; to be divided ac- 
cording to 233,114 tons gross drawn 
to 31 miles (page 540) makes „ 

Direction, offices, engineers, law expenses, 
police, rent, taxes, rates, repairs to 
vralls and fences, and petty expenses; to 
divide (page 541) according to 373,776 
tons gross and for 31 miles, makes . . '27700 



Goods. 



»» 



•52235' 



f» 



•43925 
•23705 



Total per ton gross per mile on a level 1*89614^ 

And consequently : 

Total expense per traveller per mile on a 
level, (page 541) 1-89614 x 4f§jff . . -64153 

Total expense per ^eelwe ton of goods 
per mile on a level, (page 540) 

162512 X ^ 

3'5 



ir 



•03447 



11500 



-27700 



1-62512' 



232160 



TOTAL EXPENSE OF HAULAGE. 561 

Though each of these expenses is here divided in 
proportion to the tonnage and to the length of the road^ 
it is understood that there are several among them which 
would suffer no change^ were the road longer or shorter. 
Such are the charges for loadings cartage^ offices^ &c. 
Account then should be taken of this circumstance^ were 
it desired to deduce from the data of the Liverpool and 
Manchester Railway^ what would be the expenditure on a 
different line. 

According to what has abeady been said of the effects 
of the velocity on the repairs of the engines and main- 
tenance of the road (Sect. iii. and iv. of the Appendix)^ 
it may be observed that the trains of waggons^ moving 
slower than those of coaches^ ought not^ at equal weights^ 
to cause the same wear and tear of the engines^ nor the 
same repairs to the road. As experience seems to indi- 
cate that these effects are^ for an equal tonnage^ in direct 
proportion to the velocity^ we shall here take account of 
this circumstance by separating first the expenses for 
locomotive power and maintenance of way^ each into two 
portions^ in the ratio of the tonnage and of the velocity 
on each of the two railways ; and it will not be till after 
this first partition^ that we shall perform the division of 
each portion per ton per mile, as above. This calculation 
gives the following results : — 



562 



APPENDIX. 



Partition of the eaipenaes of haulage on the Liverpool and 
Manchester Railway, taking into account the difference of 
velocity of the trains. 



Expense per ton 
gross per mile. 



TVavellcn. 



Locomotiye power: £29,607 5«. lid,, divided on a ton- 
nage of 140,662 tons gross drawn at the Telo- 
city of 20 miles an hour, for the travellers, on one 
part; — and 233,114 tons gross of goods drawn 
at the velocity of 12*5 mUes per hoor, on the 
other part (pages 540 and 541) ; — ^makes : 

For travellers £14,543 7«. lid., or per ton 
gross per mile, on a letfel (page 542) '57334' 

And for goods £15,063 ISt. Qd., or per ton 

gross per mile, on a level (page 542) 



Goods. 



ff 



Maintenance of way: £15,776 12t. Id., divided on a 
tonnage of 140,662 tons gross drawn at the ve- 
locity of 20 miles an hour for the travellers, 
on one part ; — and 374,590 tons gross of goods 
drawn at the velocity of 12*5 miles per hour, on 
the other part (page 556) ; — ^makes : 

For travellers £ 5,921 5«. Id., or -33676 

For goods £ 9,855 7«. 0<;., or 

Cartage and expenses of all kinds, above specified, and 

divided (page 560) 1*21984 



Total per ton gross per mile on a level 2*12994' 



And consequently : 

Total expense per traveller per mile on a level 
(see preceding Table, page 560) ^ 

Total expense per effective ton of goods per mile 
on a level (see preceding Table) 



-72063 



•35834* 



ft 
•20369 

•94882 



1-51085' 



It 



2*15830 



TOTAL EXPENSE OF HAULAOE. 563 

With these results^ an exact account may now be 
rendered of the profits arising from each kind of business. 
In effect, the gross receipt, for travellers, during the year, 
was 

£105,456 38. lOd., 

and the number of passengers conveyed from one end of 
the line to the other, a total distance of 30 miles, for the 
passengers, was 415,747. Thus the receipt per passenger 
per mile is 

2029 rf. 

We have just seen that the Company disburses for the 
same conveyance per mile, on a level, *7206rf.; and dividing 
the disbursement per current mile of the railway, (not on 
a level,) there would result, for this expense, 

•807 rf. 

The net profit per passenger per current mile is there- 
fore 

l-222rf. 

Again, taking the goods separately, the receipt for them 

is found to be 

£81,045 6^. U.; 

and as the work done is 151,795 effective tons carried the 
distance of 31 miles, as far as the port, the gross receipt 
per ton of goods per mile was 

4-153cf.: 

deducting, for the expenditure per current mile, relative to 
the same article, 

2-385 cf., 

there remains a net profit, per ton of goods per current 
mile, of 

l-768rf. 

We here see that, when the engines draw an effective 
ton composed of 15 passengers, they yield a net profit of 



564 APPENDIX. 

1 8*330 e(.; and that^ in drawing the same weight of goods^ 
the net resulting profit is but l*768rf.^ or the tenth part of 
the former. 

This proves that on lines established on the system of 
the Liyerpool and Manchester Railway, the chief profit is 
to be expected from travellers; and it would be a self- 
deception to reckon principally on the produce of the 
goods. Such a result indeed was to be foreseen from the 
consideration that, at the average price of places in the 
coaches, 15 passengers pay to the Company, for the trip 
between Liverpool and Manchester, the sum of 68 
shillings, whereas the conveyance of a ton of goods is 
paid only at the rate of 10 shillings and some pence for 
the same distance. 



From what has already been said of the maintenance of 
the engines and of the road, on the Stockton and Dar- 
lington Railway, it will readily be conceived that the total 
expenses of haulage are much less on that line than on 
the Liverpool and Manchester Railway. They are usually 
quoted, approximatively, as amounting to one penny per 
ton of coal carried 1 mile in the direction of the trade ; 
but as the draught in the direction of the trade, on an 
inclined line, does not give a precise idea of the effort 
exerted, it will be proper here to make the calculation 
in the same way as has been done for the Liverpool 
and Manchester Railway. 

The Company's accounts are divided imder three prin- 
cipal heads, namely: locomotive power, maintenance of 
way, and offices. 

The first comprises charges of all kinds for repairs of 
engines, engine-men's and assistants' wages, fuel, oil, 
grease, hemp, and other articles of daily consumption for 
conducting the engines and trains, llie second includes 
workmen and materials for repairs to the road, new rails. 



TOTAL BXPENSB OF HAULAGE. 565 

draining, ballasting, repairs to bridges, walls, and fences, 
and incidental expenses of the same nature. Lastly, 
the office expenses include stationery and printing, clerks, 
law disbursements, taxes, rates, police, and contingencies. 

We have already seen that during the year from 3Gth 
June, 1833, to 30th June, 1834, the expenses for loco- 
motive power amounted to 'ISSd. per ton gross per mile 
on a level (page 555); those for maintenance of way, 
including the repairs to walls and fences, were '118rf., 
as was also proved above (page 557)* There remain then 
only the office expenses, which, as will be seen, amount, 
per gross ton per mile, to '037^. 

Consequently, these three articles united give the total 
expense of haulage per ton gross per mile, on a level, at 
the velocity of 8 miles an hour, on the Stockton and 
Darlington Railway, during that year : 

Locomotive power •186'' 

Maintenance of road *118 

Office 037 

Total -341 

As however the Company's expenses, that year, were 
somewhat diminished by the circumstance that twelve of 
the engines were then nearly new, we here subjoin the 
same Company's expenses in the year following, in order 
to compare them with those of the Manchester and Liver- 
pool Railway. 

From 30th June, 1834, to 30th June, 1835, these ex- 
penses rose to the following rates : 

Locomotive Power. 

Expense per ton of goods or coals, drawn 1 mile in the 
direction of the trade, from the Company's accounts, 
-41830^; makes per ton gross per mile on a level, 

(page 549) il^El •20915*' 



566 APPENDIX. 



MakUemmce of Road. 

Expense per ton of goods or coals, drawn 1 mile, from 
the Company's accounts, '20707'; makes, per ton 
gross per mile, considering the weight of the wag- 
gons and their return empty, (page 557), 

•20707x|^ -10452 

5*25 

Office. 

Expense per ton of goods or coals, drawn 1 mile, from 
the Company's accounts, '07340^ ; makes per gross 
ton per mile, according to the same proportion as 
above -03705 



Total per ton gross per mile on a level . . '35072^ 
And pel* effective ton per mile on a level, on a rail- 
way without return of waggons empty (page 557), 

•35072 X ^- -52277 

2*65 

These expenses do not include the repairs to the wag- 
gons nor the expense for loading them, because the 
waggons on this line belong to the coal-mine proprietors, 
who bring them, moreover, to the railway all loaded and 
ready to start. It will be proper then to add here the 
former of those articles, on which the Company has con- 
served some data. 

When the Stockton and Darlington Railway Company 

let out waggons, which it did till near the end of the year 

1834, their repairs were found to amount to -^V Qf & penny, 

or '0625e(. per ton of goods carried 1 mile, or, considering 

the weight of the waggons and their return empty, to 

2'65 
•0625** X — — = •032*' per ton gross per mile. They cost 

the coal-mine proprietors still less : some of these have 
entered into a contract, on that account, at the rate of 1 5 
shillings a year per waggon. Each waggon is reckoned to 



TOTAL EXPENSE OF HAULAGE. 



567 



make^ on an average, two trips a week or 104 trips of 20 
miles each in a year, with a load of 2*65 tons. This 
bargain then makes the expense no more than *033rf. per 
ton of coal, or 'Oljd. per ton gross per mile ; but we will 
abide by the rate resulting from the Company^s books. 

Moreover, we have seen that to render the expenses 
of the Stockton and Darlington Railway comparable with 
those of the Liverpool and Manchester Railway, an ad- 
dition must be made to the former, representing the use of 
coke instead of coal. And finally, among the Liverpool 
expenses we are to take only those which occur on the 
Darlington Railway; which will exclude the articles of 
loading, cartage, and tunnel. With these alterations then, 
and taking for the Darlington Railway, the expenses of 
1834, the comparable expenses of the two railways are as 
follow : 

Total expense for haulage of goods on railways. 



Designation of the articles of 
expense. 


Expenses per ton gross of 
goods per mile, on a leveL 


On the liver- 

pool Railway, 

at the velocity 

of 12*5 miles 

per hour. 


On the Dar- 
lington Rail- 
way, at the ve* 

locity of 8 
miles per hour. 


Locomotive power 

Addition for coke instead of coal . 

Maintenance of way 

Repairs to waggons 

Offices 


•358'' 

•204 
•115 
•277 


•209*' 

•080 

•105 

•032 

•037 


Total .... 

Loading, cartage, &c 

Stationary engines and tunnels, &c. 

Total .... 


•954 
•522 
•034 


•463 


1^510 


** 



568 APPENDIX. 

It has already been observed that on the Stockton and 
Darlington Railway the waggons aire not kept with the 
same degree of neatness as on the Liverpool and Man- 
chester line. They are used only for the carriage of coal^ 
which admits of their being employed in any state. They 
are constructed too with much less nicety^ their cost price 
being but from £17 to £18^ instead of £30 or £36^ 
which those of Liverpool cost. Nor is the same expense 
bestowed on the police of the road, and on divers acces- 
sory objects. But as on a railway for slow motion^ 
destined to the conveyance of things of small value, less 
care is necessary, it may be considered that, imder the 
same circumstances, the same expenses are to be calcu- 
lated upon. 

Thus, recapitulating what precedes, with regard to the 
total expenses of working railways at great velocity, with 
simidtaneous conveyance of passengers and goods, and 
railways at small velocity destined to the carriage merely 
of materials of little value, it appears that on the former 
the expenses of conveyance for passengers will be '721 d. 
per passenger per mile on a level, and that the carriage of 
goods, exclusive of loading, cartage, &c., may amount to 
'95 d, or about 1 penny per ton gross per mile on a level; 
but if the line is exclusively destined to the carriage of 
goods, or rather to mine-work, it will be possible to 
perform the conveyance of 1 ton 1 mile on a level, ex- 
clusive of loading, cartage, &c., for *46d., or about ^ penny, 
that is, for half the preceding sum. 

Besides these expenses, which refer to the haulage 
properly so called, the loading, cartage, &c., may occasion 
an additional expense of '56 d* for every ton gross set in 
motion, as is seen by the Liverpool and Manchester 
Railway, which has furnished us with this amount. 



». 



OF HORSES AS A MOVING POWER. 569 



Sect. VI. Of the expense of horses employed as a moving 

power. 

Having shown the difference of expense existing 
between the two modes of conveyance mentioned above, 
it will perhaps be well to say a word here upon the use of 
horses. 'Hiis mode of conveyance being easy to establish, 
may in certain circumstances be useful. 

On the Stockton and Darlington Railway, where horses 
were the moving power for many years, and were still so 
in 1834, simultaneously with the locomotive engines, the 
contract passed by the Company, for the hire of horses 
with their drivers, on the principal line, was but for 
i penny per ton of goods or coal conveyed 1 mile in the 
direction of the traffic. 

To know the price resulting from this, per ton gross on 
a levely it must be remembered that one half of the 
Stockton and Darlington Railway consists of descents 
more inclined than the angle of friction, and that the other 
half is sensibly level. It follows that through half the 
way the horses have absolutely nothing to draw, and that 
through the other half they have only to exert the regular 
draught required by the same train on a leveL 

Such is the work the horses have to perform in de- 
scending the line with the loaded waggons. But moreover 
and included in the same price, they have to convey back 
the empty waggons up the line, that is to say, up an 
average inclination of -^-fs-. This work, by reason of the 
gravity on the plane, is nearly double that of drawing the 
same empty waggons on a level. 

Upon this line, then, the haulage of a waggon of goods 
1 mile requires, in consideration of the inclination and 
returns, the following traction : 

2p 



^70 APPENDIX. 



1 loaded waggon, namely, 2*65 tons of goods descending 
one mile, makes, including the waggon, 3*95 tons 
gross carried ^ mile on a level, or 1*97/. carried 1 mile 1*97/. 

The same waggon, weighing l'30^, brought back empty 
up a plane inclined -j-^, equals, by reason of the 
gravity, 3 tons conveyed the same distance on a level 3*00 

Tons gross carried to 1 mile .... 4*97/. 

Consequently the traction of 2*65 tons of goods one 
mile descending^ produces a definitive traction^ to the 
same distance on a levels of 4*97 tons, or 1*88 times as 
much. The proportion is less here than in the case of 
locomotive engines, because the weight is less by that of 
the engines and their tenders. 

Since the price paid for the hire of horses is '50 rf. for the 
conveyance of 1 ton of goods 1 mile, it follows that the 
locomotive power per ton gross per mile, on a level, 

amounts to ='267^. 

1-88 

Consequently, adding the other articles above, we have 
for the total expense of haulage relative to the use of 
horses as a moving power ; 

Hire of horses and drivers, or locomotive power . . . '267' 

Maintenance of the road, as above '105 

Offices, as above -037 

Repairs to waggons, as above *032 

Total per ton gross per mile on a level, exclusive of 

loading, &c •441*' 

3*95 
And per eflectivc ton per mile on a level, '441** x — — •657* 

^ 2-65 

We perceive that these expenses are more considerable 
than those of the Stockton and Darlington Railway 
locomotive engines, with the use of coal, but nearly equal 
to what would be necessary with the same engines, if coke 
were used. 



NET PROFITS. 571 



Sect. VIL Of the net profits. 

Before we pass on to the specified statements of the 
receipts and expenses of all sorts of the Liverpool and 
Manchester Railway Company^ we shall take down here, 
from those same statements, the amount of the profits 
made by the Company, from the opening of tiie railway. 
This sketch will show that, if the mode of haulage in 
question necessitates considerable expenses for its esta- 
blishment, the profits it produces are fully adeqtiate to 
indemnify speedily the Shareholders. 

The road was opened to trade on September 16th, 
1830, and from that period the dividends per share of 
£100 sterling amounted to the following sums : 

December 31, 1830 £2 

Jane 30. 1831 4 10 

December 31, 1831 4 17 8 

Jmie 30, 1832 448 

December 31, 1832 4 8 

June 30, 1833 476 

December 31, 1833 (besides a reserved 

fund of £4,088 8«. lOcf.) 4 15 3 

June 30, 1834 4 15 2 

Total Sum from Sept. 16, 1830, to June 30, 
1834, or in three years, nine months and 
a half £33 18 3 

This sum makes 9 per cent, per annum, notwithstanding 
the reserved fund set apart by the Company, and the 
extraordinary expenses inevitable at the outset of an 
undertaking, which being the first of its kind, was neces- 
sarily obliged to pay dearly for its own experience, whilst 
future Railway Companies will have only to profit by the 
experience acquired by their predecessors. 

Besides this high interest for the capital invested, the 
shares of this railway, from the original price of JCIOO 



572 APPENDIX. 

sterling, had risen^ after four years' establishment only^ to 
£210; and have since been continually rising: and those 
of the Stockton and Darlington Railroad bring in 8 per 
cent, interest, and have risen in the short interval of 
9 years from £100 to £300. 

These plain facts make it unnecessary for us to add any 
reflections. 

We shall be happy if the elucidations already giv^en 
with regard to expense, be of use to persons who may feel 
inclined to engage in these speculations, which cannot SbuI 
to be as advantageous to their private fortune as to the 
prosperity of the country at large. But, to render this 
part of our subject more complete, we shall conclude this 
Appendix by giving the specified statements of the re- 
ceipts and expenditure of the Liverpool and Manchester 
Railway Company, from its origin, in September, 1830, till 
the 30th June, 1834, at which period the Directors ceased 
to render detailed accounts to the Shareholders. 



EXTRACTS 

PROM THE 

REPORTS OF THE DIRECTORS OF THE LIVERPOOL 
AND MANCHESTER RAILWAY. 

PROM THE 

Opening of the RaUway, on the 16M September, 1830, to the 

ZOth June, 1834. 



STATEMENT OF EXPENDITURE ON CAPITAL ACCOUNT. 

Amount of expenditure on the construction of the way and the 
works, from the commencement of the undertaking to 3l8t 
December, 1833 £1,089,818 17 7 



ANNUAL OR WORKING ACCOUNT. 

PROM 16th SKPTSMBRR to 31st DICIMBIR, 1830. 

Net profits of the Compi^ny £14,432 19 5 

Dividend per share of £100 200 

BALP-TBAR ENDING 30tH JUNB, 1831. 

Net profits of the Company £30,314 9 10 

Dividend per share of £100 4 10 

HALF-TEAR ENDING 31 ST DECEMBER, 1831. 

Tons. 
Merchandise between Liverpool and Manchester . . . 52,224 

Road traffic 2,347 

Between Liverpool and the Bolton junction 10,917 

Coal from Huyton, Eltonhead, and Haydock collieries, 

brought by the Company's engines 7,198 

Coal from Uulton brought by the Bolton engines . . . 1,198 



574 APPENDIX. 



Number of passengere booked at the Company's 
offices 256,321 

Number of trips of 30 miles performed by the 
locomotive engines with passengers .... 2,944 

Do. with goods 2,298 

Do. with coals 150 



Coach department £58,348 10 

General merchandise 30,764 17 8 

Coal department 695 14 4 

£89,809 2 O 

Expentet, 

Office establishment £902 3 10 

Coal disbursements 60 15 5 

Petty ditto 110 5 

Cart ditto 60 17 8 

Maintenance of way 6,599 12 6 

Charge for direction 297 19 

Coach office establishment 589 5 9 

Locomotiye power 12,203 5 6 

Advertising 59 3 4 

Interest 2,737 7 3 

Rent 900 5 3 

Compensation (coaching department) 156 7 5 

Engineering department 625 

Carrying dUbursements 10,450 12 3 

Taxes and rates 2,763 5 I 

Stationary engine disbursements 269 4 7 

Coach disbursements 6,709 7 11 

Waggon ditto 979 19 8 

Compensation (carrying department) 786 8 2 

Police establishment 1,490 14 1 

Law disbursements 98 9 10 

Bad debts 175 13 6 

£49,025 18 5 



Net profit from Ist July to 3l8t December, 1831 . . £40,783 3 7 

Dividend per share of £100 4 10 

Net profit on Sunday travelling per share of £100 . . 7 8 



HALP-YKAK ENDING 30tH JUNK, 1832. 

Tons. 
Merchandise between Liverpool and Manchester . . . .54,174 

Traffic to and from different parts of the road 3,707 

Between Liverpool and the Bolton junction 14,720 

Coals from different parts of the road brought by the 

Company's engines 22,045 

Coals brought by the Bolton engines 7,411 



RECEIPTS AND EXPENDITURE. 



575 



Number of passengers booked at the Company's 

offices 174,122 

Number of trips of 30 miles performed by loco- 
motive engines with passengers 2,636 

Ditto with merchandise 2,248 

Ditto with coals 234 

Coaching department JC40,044 14 

General merchandise department 32,477 14 

Coal ditto 2,184 7 



7 

6 



£74,706 16 1 



Coach 
disbursem^. 



Carrying 
disbursem^. 



ExpeniBU, 

Bad debt account 

r- Guards' and porters' wages, ^ 
£1,104 4 6.~Parcel carts and 
drivers' wages, £254 10 5.— - 
Omnibuses and duty, £1,082 7. 
— Repairs and materials, £1,777 
9 4. — Gas, oil, tallow, &c., £228 
14 6. — Stationery and sundry 

disbursements, £441 1 7 

Salaries, £1,749 5 lO.—PortersS 
wages, £3,862 8.— Brakes- 
men's wages, £461 5 9. — OU, 
tallow, cordage, &c., £461 12 6. 
—Carting, £808 16 5.— Repairs 
to jiggers, trucks, &c., £163 14 
11. — Stationery and sundry ex- 
^ penses, £503 10 8 

Coal ditto 

Cartage (Manchester) 

Charge for direction 

Compensation (coaching) 

Compensation (carrying) 

Coach office establishment (Salaries, £573 13 1. — 
Rent and taxes, £106 10 0.) 

Engineering department 

Interest 

Fuel and watering, £2,957 8 0. 
— Oil, tallow, hemp, &c., £507 
3 1. — Repairs and materials, 
£5,947 6 5. — Enginemen's wa- 
ges, £1,170 18 8 

Maintenance of way (wages, £3,929 8 0.— Blocks, 
sleepers, chairs, &c., £2,668 12 3. — Ballast, 
£733 3) 

Office establishment (Salaries, £652 8 6.— Rent and 
taxes, £77 9 2.— Stationery, &c., £81 10 5) 

Police and gatekeepers 

Petty disbursements 

Rent 



394 5 7 



* 4,888 11 



* 8,010 6 9 



Locomotive 
power. 



26 8 10 

1,420 4 9 

308 14 

101 10 9 

288 10 3 

680 3 1 

520 9 

5,966 14 11 



10,582 16 2 



7,331 6 

811 8 1 

1,356 9 11 

75 1 

1,840 1 10 



576 



APPENDIX. 



Stationary engine and tunnel disbiinements, new 
tunnel rope, £330 10 S.^Coal, Je265 7 0.— 
Wages, £290 9 9.— Bepairs, ml, tallow, hemp, 

&c., £165 8 9 £1,051 16 2 

Taxes and rates 1,109 14 9 

Smiths' and joiners' wages, £586 ^ 
6 7. — Iron, timber, &c., £265 
9. — CauTass, paint, &c., for 
sheets, £155 10 10 



Waggon 
disbursem**. 



*• 1,006 18 2 



47,770 15 5 
Deduct credits 1,112 4 1 



<£46,(»S8 11 4 



Net profits tor six months :£28,048 4 9 

Dividend per share of £100 400 

Net profit on Sunday traTelling per share of £100 . . 4 8 



HALT-TEAR ENDING 31ST OKCEMBER, 1832. 

Tons. 
Merchandise between Liyerpool and Manchester .... 61,995 
Ditto to diiTerent parts of the road, including the 

' Warrington and Wigan trade, .... 6,01 1 

Ditto between Liverpool and Bolton 18,836 

Coals from various parts of the road to Liverpool or Man- 
chester 39,940 

Number of passengers booked in the Company's 

ofllces 182,823 

Number of trips of 30 miles performed by the lo- 
comotive engines with passengers .... 3,363 

Do. with goods 1,679 

Do. with coals 211 



Receipts. 

Coaching department £43,120 6 11 

General merchandise 34,977 12 7 

Coal department 2,804 3 4 



Expeiuee, 

Bad debt account 

^Guards' and porters' wages, -^ 
£1,173 19 6. — Parcel carts 
and drivers' wages, £375 14 4. 
— M'aterials for repairs, £464 
1 9. — Men's wages, repairing, 
£613 18 1.— Gas, ofl. taUow, ^ 
&c., £232 11 7.— Duty on pas- 
sengers, £985 19 L— Station- 
cry and petty expenses, £414 

'^ 19 7 



Coach 
disbursem^. * 



£80,902 2 10 



£81 6 



4,261 3 11 



RECEIPTS AND EXPENDITURE. 



577 



Carrying 
fUsbusem**. 



Locomotive 
power. 



SaUries, £1,822 13 2.->Por. 
ter»', &c., wages, £3,925 7 4.— 
Gas, oil, tallow, cordage, &c., 
£296 11 r.—Repairs to jig- 
gers, tracks, stations, &c., £398 
3 11. — Stationery and petty ex- 
penses, £540 13 5 .... 

Coal ditto 

Cartage (Manchester) ' 

Charge for direction 

Compensation (coaching) 

Ditto (carrying) 

Coach office establishment (Salaries, £556 3 10.— 
Rent and taxes, £75 15 2) 

Engineering department 

Interest 

" Fuel and watering, £3,848 10 8. 
—Oil, tallow, hemp, &c., £661 
1 9. — Materials for repairs, 
£3,723 9 7.— Men's wages, re- 
pairing, £3,352 16 2.— Engine 
and firemen's wages, £1,060 

in 6 

Law disbursements 

Maintenance of way (wages, £3,675 16 5. — Blocks, 
sleepers, chairs, dec, £2,355 17 1. — BaUast, &c., 

£846 10 9) 

Petty disbursements 

Rent 

Stationary engine and tunnel disbursements, (Coal, 
£209 15 3. — Engine and brakesmen's wages, 
£316 7 5.— Repairs, gas, oO, tallow, &c., £326 

14 7) 

Taxes and rates 

Smiths' and joiners' wages, £583 " 
5. — Iron, timber, &c., £350 
12 10. — Canvass, paint, &c., for 

sheets, £31 

Office establishment (Salaries, £623 18 0. — Rent, 

£85 0.— Stationery, £18 9 0) 

Police ditto 



Waggon 
cUsbursem^. 



> 6,983 9 5 



27 2 10 

2,744 18 7 

295 1 

209 15 11 

150 19 11 

631 19 

450 

4,555 15 7 



12,64« 9 8 



118 3 8 



6,878 4 3 

66 2 

1,246 5 



852 17 3 
3,483 18 2 

964 13 3 



727 7 
902 16 5 



Net profit for six months 

Dividend per share of £100 

Net profit on Sunday travelling per share of £100 



£48,278 8 10 

£32,623 14 

4 4 

4 



BALr-YBAR ENDING 30tH JUNK, 1833. 

Tons. 
Merchandise between Liverpool and Manchester .... 68,284 
Ditto to different parts of the line, including War- 
rington and Wigan 8,712 

Ditto between Liverpool, Manchester, and Bolton . 19,461 
Coals from various parts, to Liverpool and Manchester . . 41,375 



578 



APPENDIX. 



Total number of passengers booked in the Co/s 
offices 171,421 

Number of trips of 30 miles performed by the 
locomotive engines with passengers .... 3,262 

Ditto with merchandise 2,244 



Receipts. 



Coaching department .£44,130 17 2 

Merchandise ditto 39,301 17 3 

Coal ditto 2,638 15 9 



X86,07I 10 2 



Eapensef, 



Coach 
disbursem'*. 



Advertising account 

Bad debt account ......... 

^Guards' and porters' wages, -^^ 
£1,150 4 0. — Parcel carts, 
horse keep, and drivers' wages, 
£401 18 6.— Materials for re- 
pairs, £383 15 11. — Men's 
wages, repairing, £758 10 6. 
— Gas, oil, tallow, cordage, &c., 
£324 4 0. — Duty on passengers, 
£2,466 15 4. — Stationery and 
petty expenses, £236 15 6. — 
Taxes on offices, stations, &c., 

^£112 18 4 

"Agents' and clerks' salaries," 
£1,703 17 6. — Porters' and 
brakesmen's wages, horse keep, 
&c., £4,687 9 7.— Gas, oil, 
tallow, cordage, &c., £648 4 
» 11. — Repairs to jiggers, trucks, 
stations, &c., £405 13 l.-> 
Stationery and petty expenses, 
£336 9 0. — ^Taxes, insurance, 
&c., on offices and stations, 
L£798 18 

Coal disbursements 

Cartage (Manchester) 

Charge for direction 

Compensation ^coaching) 

Compensation (carrying) 

Coach office establishment (Agents' and clerks' sa- 
laries, £577 19 6.— Rent and taxes, £102 17 1) 

Engineering department 

Interest 



£50 8 7 
176 18 6 



> 5,835 2 1 



Carrying 
disbursem^. 



» 8,579 15 9 



120 16 
2,460 16 

252 

38 1 

1,033 18 


1 
1 

2 
3 


680 6 

441 17 

5,367 11 


7 

4 
9 



RECEIPTS AND EXPENDITURE. 



579 



Locomotive 
power. 



> 14,715 16 9 



Coke and carting, £2,795 4 5. 
— Wages to coke fillers, and 
watering engines, JS338 16 10. 
— Gas, oil, tallow, hemp, &c., 
J6760 15 2. — Copper and brass 
tubes, iron, timber, &c., for 
repairs, £3,290 8 8. — Men's 
wages, repairing, £4,115 8. 
Enginemen and firemen's wages, 
£892 4 4.— Outdoor repairs to 
engines, £943 6 8. — ^Two new 
engines, " Leeds" and " Firefly," 

£1,580 

Maintenance of way (wages, £3,648 18 5. — Blocks, 
sleepers, cheiis, &c., £2,052 5 11. — Ballast and 

draining, £1,013 4 11) 6,714 

Ofiice establishment (Salaries, £624 19 0.— Rent 
and taxes, £62 18 6.— Stationery, &c., £56 

19 5) 

Police 

Petty disbursements 

Rent 

Repairs to vralls and fences 

Stationary engine and tunnel disbursements (Coal, 
£155 8 1. — Engine and brakesmen's wages, £363 
8 10.— Repairs, gas, oU, Ullow, &c., £340 15 11) 

Tax and rate 1,891 

Waggon disbursements (Smiths' and joiners' wages, 

£598 3 1.— Iron, timber, &c., £320 1 4.— Cord- 

age, paint, &c., for sheets, £82 7 3) .... 

Cartage (Liverpool) 



744 
950 
70 
601 
296 



859 



9 3 



16 
4 


15 
4 



12 




1,000 11 
18 4 



11 
7 

8 
2 



10 
7 



8 
6 



£52,900 9 1 



Net profit for six months 

Dividend per share of £100 

Net profit on Sunday travelling per share of £100 



£33,171 1 1 
4 4 
3 6 



HALV-YKAR ENDING 31ST DECEMBER, 1833. 



Tons. 
Merchandise between Liverpool and Manchester .... 69,806 
Ditto to and from different parts of the line, includ- 
ing Warrington and Wigan 9,733 

Ditto between Liverpool, Manchester, and Bolton . 18,708 
Coal from various parts to Liverpool and Manchester . . 40,134 
Total number of passengers booked at the Co«'s 

ofiSces 215,071 

Number of trips of 30 miles performed by the 

locomotive engines with passengers .... 3,253 
Do. with merchandise 2,587 



580 



APPENDIX. 



Heceipts. 

Coaching department £54,685 6 11 

Merchandise ditto 39,957 16 8 

Coal ditto 2^91 6 6 



Je9 7,234 10 1 



Expenset, 



Advertising account 
Bad debt account 



6 10 
374 10 



Coach 
disbursem^. ' 



Carrying 
disbursem^. 



"Guards' and porters' wages, 
£1,168 4 6. — Parcel carts, horse 
keep, and drivers' wages, JS361 

I 7. — Materials for repairs, 
£689 12 6.— Men's wages, re- 
pairing, £1,041 1 3.— Gas, oil, 
tallow, cordage, &c., £196 4 11. 
— Duty on passengers, £3,224 

II 11. — Stationery and petty 
expenses, £277 4 5. — Taxes 
on offices, stations, &c., £116 
8. — Guards' clothes, £64 
15 0.* 

"Agents' and clerks' salaries, 
£1,728 16 9. — Porters' and 
brakesmen's wages, horse keep, 
&c., £5,006 6 10.-— Gas, oil, tal- 
low, cordage, &c., £529 17 0. — 
Repairs to jiggers, trucks, sta- 
tions, &c., £366 9 11.— Sta- 
tionery and petty expenses, £429 
5 1. — ^Taxes and insurance on 
offices, &c., £456 17 7.— Sacks 
(^forgndn, £110 3 10 .... 

Coal disbursements 

Cartage (Manchester) 

Charge for direction 

Compensation (coaching) 

Compensation (carrying) 

Coach office establishment (Agents' and clerks' sa- 
laries, £602 6 8.— Rent, £30) 

Engineering department 

Interest 

f Coke and carting, £3,197 4 4. 
— ^Wages to coke fillers and 
waterers, £348 8 5. — Gas, oil, 
tallow, hemp, cordage, &c., 
£865 14 9. — Brass and copper, 
iron, timber, &c., for repairs, 
£3,755 3 7.— Men's wages, re- 
pairing, £4,401 4 10.— Engine 
and firemen's wages, £784 8 5. 
— Out-door repairs to engines, 
£613 3 9 



Locomotive 
power. 




1 



* 7,138 16 9 



' 8,627 17 



82 9 

3,173 18 

312 18 

142 4 8 

223 10 11 

632 6 8 

319 3 4 

5,140 6 4 



> 13,965 8 1 



1 



RECEIPTS AND EXPENDITURE. 



581 



Mainte- 
nance of 
way. 



^ 6,425 14 8 



^ Wages to plate-layers, joiners,^ 
&c., £2,937 19 2. ~ Stone, 
blocks, sleepers, keys, chairs, 
&c., £2,411 2 4.-> Ballasting 
and draining, £925 16 11. — 
^ New rails, £150 16 3 . . . . 
Office establishment (Salaries, £607 2 0.— Rent 
and taxes, £75 14 3. — Stationery and printing, 

£22 7 8.->Stamps, £17 2 3) 

Police 

Petty disbursements 

Rent 

Repairs to walls and fences 

Stationary engine and tunnel disbursements, (Coal, 
£302 6 5. — Engine and brakesmen's wages, 
£319 11 2. — Repairs, gas, oil, tallow, &c., 
£419 15 5.— New rope for tunnel, £266 3 6) . 

Tax and rate 

" Smiths' and joiners' wages, £718 
19 7. — Iron, timber, castings, &c., 
£700 9 1.— Cordage, paint, &c., y I fill 3 
£28 5 2.~Canyas8 for sheeta, 

L £163 6 5 

Cartage (Liverpool) 

Law ^bursements 



722 6 2 

1,022 7 6 

61 19 6 

603 10 8 

665 3 4 



1,307 16 6 
3,409 11 



Waggon 
disbursem**. 



80 17 10 
300 3 9 



Net profit for six months 

Dividend per share of £100 

Net profit on Sunday travelling per share of £100 
Reserved fond formed in the six months . . . 



£56,350 1 9 

£40,884 8 4 

4 10 

5 3 

4,088 8 10 



HALF-YBAR ENDING 30tH JCNX, 1834. 

Tons. 
Merchandise between Liverpool and Manchester .... 69,522 
To and firom different parts of the road, including Warring- 
ton and Wigan 15,201 

Between Liverpool, Manchester, and Bolton 19,633 

Coal to Liverpool and Manchester 46,039 

Number of passengers booked at the Company's 

offices 200,676 

Number of trips of 30 miles performed by the 

locomotive engines with passengers .... 3,317 
Ditto with merchandise 2,499 

Coaching department £50,770 16 11 

Merchandise ditto 41,087 19 5 

Coal ditto 2,925 15 11 

Experuei. 

Advertising account £16 15 

Bad debt cUtto 75 12 3 



£94,784 12 3 



582 



APPENDIX. 



Coach 
disbarsem^. 



Carrying 
disbursem**. 



Guards' and portera' wagea»<^ 
£1,167 11 10.— PaitMd carta, 
horse keep, and drivers' wages, 
£359 13 0.— Materials for re- 
pairs, £1,007 9 7. — Men's wages, 
repairing, £1,221 15 5.— Gas, 
oil, tallow, cordage, &c., £358 
15 6. — Duty on passengers, 
£3,008 1 11.— Stationery and 
petty expenses, £165 2 5. — 
Taxes, insurance, &c., on offices 
and stations, £65 8 11 ... 
^Agents' and clerks' salaries,'' 
£1,740 14 2. — Porters' and 
brakesmen's wages, horse keep, 
&c., £5,397 8 5. — Gas, oil, 
tallow, cordage, &c., £708 17 4. 
— Repairs to jiggers, trucks, sta- 
tions, &c., £716 2 8. — Sta- 
tionery and petty expenses, 
£290 3 2.— Taxes, insurance, 
&c., on offices and stations, 
£469 6 2 ^ 

Coal disbursements 

Cartage (Manchester) 

Charge for direction 

Compensation ^coaching) 

Compensation (carrying) 

Coach office establishment (Agents' and clerks' sa* 
Uiries, £615 1 11.— Rent and taxes, £63 1 1) . 

Engineering department 

Interest 

" Coke and carting, £2,882 11 4. 
— Wages to coke fillers, and 
watering engines, £386 19 5. — 
Gas, oil, tallow, hemp, &c., £881 
18 4. — Copper and brass tubes, 
iron, timber, &c., for repairs, 
£4,140 19 6.— Men's wages for 
repaiiing, £5,432 8 8. — ^Engine- 
men and firemen's wages, £836 
14 3. — A new engine, £700. — 
Lathe engine, boiler and fixing 
for repairing sheds and watering 
t. stations, £380 6 4 ^ 

Law disbursements 

^ Wages and small materials,.^ 
Twioi-«#* £4,221 2 5.— Stone, blocks, 

n2n^ of J "^««P«"' ^'* ^^'^®2 18 7— 
nance or < ^^^ ^^^ ^^ ^^. __._._ 



7,353 18 7 



9,322 11 11 



45 1 

2,988 6 2 

289 16 

26 3 10 

645 6 

678 3 

352 10 

5,546 4 



Locomotive 
power. 



* 15,641 17 10 



way. 



i, points, r 

14 5.— 
t93 2 .^ 



100 



9,350 17 5 



crossings, &c., £3,153 
^ Ballast and leading, £493 
Office establishment (Salaries, £818 14 4.— Rent 

and taxes, £58 8 0) 

Police 

Petty disbursements 

Rent 



877 2 4 

1,016 18 1 

60 

363 11 11 



RECEIPTS AND EXPENDITURE. 



583 



Stationary engine and tunnel disbursements, (Coal, 
;6327 12 1. — Engine and brakesmen's wages, 
£3Sb 7 0.— Repairs, gas, oU, tallow, &c., £273 

111) 

Tax and rate 

^Smiths' and joiners* wages, 

£773 3 8.— Iron, timber, &c., 

£728 12 4.— Cordage, paint, 

&c., £109 19 2.— Canvass for 

[^ sheets, £240 

Repairs to walls and fences 

Cartage (LiYerpool) 



Waggon 
disbursem**. ** 



986 10 2 
1,778 16 10 



1,851 15 2 



644 11 
80 17 6 



Net profit for six months 

Dividend per share of £100 

Net profit on Sunday travelling per share of £100 



£60,092 15 11 

£34,691 16 4 
4 10 
5 2 



THE END. 



PRINTED BY W. HUOHB8, 

king's head court, OOUOH SQOARK. 



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ON STEAM NAVIGATION. 

These very important and interesting volumes, comprising 125 very elaborate and beautifully engraved 
Plates, are, in Sections, Elevations, Plans, Details, &c., of the highest utility to the Engineer and 
Student, to Manu^turers of Marine, Locomotive, and Land Engines ; — ^the science being elnddated 
and explained by the most eminent practical men of Britain. In 2 4to. vols., price £4. 4#., entitled 

THE STEAM ENGINE; 

Comprising an account of its invention and progressive improvement, vrith an iNTSsnoAnow of iu 
PRINCIPLKS, and the proportions of its parts for kppicibnct and streno'th ; detailing also it^ 
application to Navigation, Mining, Impelling Machines, &c., and the Result in mtmeioiu Tables 
for Practical Use, with Notes, Corrections, and New Examples, relating to Locomotive and other Engines. 

Rbvisbii and Edited by W. S. B. WOOLHOUSE, F.R.A.S., &c 

The algebraic parts transformed into easy practical Rules, accompanied by Examples familiiri) 
explained for the Working Engineer, with an ample 

APPENDIX, 
Containing, besides a vast acquisition of Practical Pinters, an Elementary and Practical Description of 
Locomotive Engines now in use, illustrated by Examples ; and the Principles and Practicse of Steaii, 
for the purposes of Navigation either in Rivers or at Sea ; showing its present and progressive state, by 
illustration of the various Examples of Engines constructed for Sea, War, and Packet Vessels, and River 
Boats, by the most eminent MaJcers of England and Scotland, drawn out in Plans, Elevations, ScetkmSf 
and Details, with a Scientific Account of each, and on 

STEAM NAVAL ARCHITECTURE, 
Showing, by existing and the latest Examples, the Construction of War, Sea, and Packet VesMls : their 
Naval Architecture, as applied to the Impelling Power of Steam for Sea and River purposes. This 
portion of the work is edited by several very eminent Ship Builders — 

OLIVER LANG, Esq., of H.M. Dock-yard, Woolwich, 
J. FINCHAM, Esq., H.M. Dock-yard, Chatham. 
T. J. DITCHBURN, Esq., Depfifozd and BlackwaU. 

The new subjects in this edition consist of the works of 

Messrs. Boidton and Watt William Morgan, Esq. 

The Butterley Company. Messrs. Hall, Dartford. 

Messrs. MaudsUy, Sons, and Field. Edward Bury, Esq., liverpooL 

Messrs. Seaward. Messrs. Hague. 

Robert Napier, Esq., Glasgow. Messrs. Claude, Girdwoord, and Co. 

Messrs. Fairbaim and Murray. Messrs. R.Stephen8on and Co.,Newc8Stlettp<mTyne. 

Bttsiaiitts^ &9 ^tvmMian^ to fger ^iUieirts. 

LIST OF PLATK8. 

1. iMnneCriealpnycetlaiiof ftfceteBgularttesmboilar. 

2. Two MetioiM of a cylindrical steam boiler. 

3. Brunton'a apparatoa for feeding furnaces by machinery. 

4. High prenure engine with four-paMaged cock. 

6. Section of a doable acting condensing engine for work- 
ing ezpansiTely. 

0. Section of a common aimoapheric engine. 

7. Represents the construction of pistons. 

8. Parts of Fenton and Murray's double engine. 

9. Apparatus for opening and closing steam passages. 

10. (A). 10 (B). Parallel motiooa or eombinatums oaed to 
produce rectilinear motion from motion in a circular arc. 

11. Plan and elevation of an atmospheric pompiag engine 
for rainng water fkom a mine. 

IS. Boolton and Watt's single acting engine. 

IS. Double acting engine for raisins water. 

14. ^for impelling machinery, by Fen- 



> 



ton, Murray ft Co. 
15. Maudslay's portable engine. 
lO. Indicator for measuring the foree of steam in the 

cvlinder. 
-^Diagrami to iUnstrafee Che comparathre stability of 

opposite diiifs of vessels. 

17. Sectitm of a steam vessd with its boiler in two parts. 

18. Isometrical projection of a steam boat engine as first 
arranged br Boulton and Watt. 

19. Section and plan of steam boat engine. 



M. Side elevadon and 
91. Kingston's valves. 

blow-off valves. 

iiyection valres. 

hand pump valves. 

as. Boilers of Her Muesty's steam vessel 

53. Boilers of Her Mucsty's steam frigate Medea. 

54. Paddle wheels of Momn and Seaward. 

55. Positions of a float 01 a radiating whed. and also of a 
vertical acting wheel, in a vessel m motioo. 

96. Qydoidal paddle wheel fitted to the Great Western. 

27, 98. Illustrate Captain Oliver's paper. 

99. ExhibUs the various situations cSf a trial at sailing ftf 

the Medea, with the Caledonia, Vancnaid, and Asia. 
SO. Side view oS the engines of the Red Bover, and Citr^ 

Canteibury, steam vessels* 
31. Longitudinal section of ditto. 

39. Cross section of engines of ditto. 

8S. Side devaCion of the enf^ of the NBe ateam sh^^. 

84. Plan of the engine of the Nile. 

35. SO. Cross sections of engines of the NQe. 

37, S8, 89. Enoines of Her Mi^esty's sleam ft%al» Aomb. 

40. Engines of the Ruby Gravesend padbst. 

41. Seraon oS one of the engines of the Dosi Joan Ptain> 
sula Company*s packet. 

43. BoUers of Her Mi^ty's ships Hcnnca, Sjpstfife, and 
Firefly. 



4 



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ARCHITECTURAL. LIBRARY, 59, HIGH HOLBORN. 



3 



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■g;v 



j^ 



i. 



44, 45, 46. Elevation, plan, and two aectioa* of the 

enginea of the armed Ruaaian steam ships Jaaon and 

Colchis. 

48. Hall'a improvementa on steam enginea. 
50. Enginea m Her M^jeatj's steam ship If enenu 

68, 53, 54. Engines of the Hull and London packet 

William WUbexforee. 
(A). Longitudinal aeetion of Humphiys's patent marine 

engine. 

(B). Longitudinal eleration of Humphrya's marine 

engine. 

(A). Midahip section of the steam packet Dartford, 

ahowing a nont deration <rf a pair of Humphrys's 

engines. 

(B). Flan of the engines of the Dartford. 
58, 50. Forty-five horse power engine, constructed by 

W. Fairbaim and Co. 

61, 03, 63. Ten-hone power engine, eonatmeted by 

W. Fairbaim & Co. 

Elevation of a locomotive engine, Stanhope and Tyne 

Riulway; constructed by Messrs. B. Stq»henaon and 

Co., of^Newcastle upon Tym* 

Secdon of ditto. 

Safety valvea of ditto. 

(A). Cylinder oorwr and eonneetiBg rods of ditto^ 

(B). Cylinder and piston at large or ditto. 

Plan and section of boiler seating for a twenty-horse 

engine, at the manufactory of Messrs. Wbitworth and 

Co., Mancheater. 

Messrs. Hague'a double acting cylinder, with slides, &c. 



'.,, * The flnt publication of Mr. Tredgold's work, 
r^n one of the most important mechanical and 
" cientific subjects of oiir age, was so highly suc- 
ressfiil, that, besides being translated into the 
Prench, and, we belieTe, other languages, a new 
ifsdition was imperatively called for. That call 
?ha8 been answered by the present enlarged work, 
in which has been embodied the progress and 
improved application of that mighty agent Steam, 
an investigation of its principles, and a practical 
view of its uses and effects in steam vessels, steam 
carriages, and railroads. When we look around 
us and see the face of the country changed and 
changing; the expedition of a week compressed 
into a single day; the limits of pleasure and of 
business widely extended among all classes of 
society; new wants created, and new wishes 
gratified; sedentary easily and readily converted 
' into ambulatory life ; the sphere of ci^ homes, as 
it were, enlarged by a circle of rural miles;'- 
when, in fsct, we see the prodigious alteration 
made in our social, statistical, economical, po- 
litical, national, and international system, by the 
growing powers of this vast engine, we cannot 
but consider the effort to offer us a just and com- 
prehensive account of it to be one of the most me- 
ritorious within the scope of individual industry, 
skill, and labour. We, therefore, think the public 
deeply obliged to Mr. Tredgold, the author, and 
Mr. Weale, the enterprising publisher, who must 
have expended a very large sum on the risk, for 
the very important volumes now before us. 

* It is apparent that it is a publication of great 
magnitude and great worth. Above a hundred 
plates of steam engines, &c. &c., illustrate its 
descriptions; and many wood-cuts serve further 
to render the contents plain and intelligible to 
every capacity. Thus the actual operations of 
such men as fioulton and Watt, Maudslay and 
Field, Seavrards, Napier of Glasgow, and other 
eminent mechanicians, and, we may add, en- 

^ 



70, (A). 70 (B). Sections of the engines of the Berenice 
steam vessel. 

71, 7S. Beale's patent rotatory engine. 

73. Mr. Ayre's contrivance for preventing a locomotive 
engine from running off a railway. 

74 to 83. Belate to the very important subject of aU kinds 
of paddle wheels. 

84 to 88. Sixty-five inch cylinder engine, erected by 
Messrs. Maudslay, Sons, and Field, at Chelsea water- 
works. 

89 to 02. Patent locomotive engine, made by Meaars. R. 
Stephenson and Co. for the London and Birmingham 
Railway. 

98. Drawings of the Comet, the first steam boat in Europe. 

94. The Pacha's steam vessel of war, the Nile. 

95, 90. The Hon. Eaat India Company's steam vessel 
Beremce. « 

97. Draught of the Forbes steamer, Chineae rigged. 

98. Heme Bay steam packet Red Rover. 

99. Diamond Company's steam packet Baby. 

100 to 103. Her M igeaty's steam veasel of war Medea. 

104 to 107. Conatruetion of the Nile ateam ship, built for 

the Pacha of Egypt. 
108, 109, 1 10. His Imperial Majesty's armed ateam veaael 

Colchis. 
Ill, 111 (A). Enffinea of the steam ship Tiger. 
1 la. The Admiralty yacht Firebrand. 

113. Portrait of the late Mr. Watt. 

1 14. Portrait of the late Mr. Tredgold. 

115. 117, 118. Illustrate steam navigation in America. 



lightened philosophers as well as experienced 
artisans, are explained to us, and set before our 
eyes so as to be palpable to the understanding. 
In the same way the locomotives of the Messrs. 
Stephenson, of Newcastle, the construction of 
the elegant government steam boats of Mr. Lang, 
of Woolwich, and Mr. Fincham, of Chatham, (ves- 
sels it is a delight to notice as we pass up or 
down the river,) are rendered familiar to us ; and 
we care little to vex ourselves about hypothetical 
improvements and untried experiments. We have 
witnessed so many pseudo certain and undeniable 
inventions fail, that we have become rather scep- 
tical when we hear of patents that are to supersede 
all that has been done before, or listen to the dic- 
tatorial laws of people whom we have known to 
be more frequently wrong than right. We are 
glad to observe, however, that in this new edition 
most of the errors of the former have been cor- 
rected; and what questionable statements or 
mistakes may remain are not such as to impeach 
the vast utility of the publication. 

' The Appendix, indeed, is deserving of much 
praise. The rules of practice are well expounded, 
and the mathematical calculations, remodified into 
simple arithmetic, are excellent for the purpose of 
enabling the working man ("operative'' is the 
fsshionable phrase) to perform. his duty. 

' Upon the whole, not to dwell upon either real 
or supposed imperfections, inseparable from a 
production embracing so vsst a number of com- 
plicated matters — a production treating of things 
in an almost daily state of partial transition — ^we 
feel bound to pronounce this treatise to be a very 
able and satisfactory exposition of the state of 
steam navigation and railroad travelling to the 
present time ; and as such we heartily recommend 
it to the public at large, both at home and on the 
continent, where its predecessor has hitherto been 
esteemed a standard work.' — Literary Gazette, 
Auguet 3, I839. 



4 



WORKS PUBLISHED BY JOHN WBALE, 



4. 
In 2 vols., very neatly half-bound in morocco or rossia, gilt tops, Price JC5. 5«. 
TREDGOLD ON THE STEAM ENGINE AND ON STEAM NAVIGATION 



5. 

In 2 vols.! elegantly bound in russia or morocco, gilt leaves, Price JC5. 15s. 6dL 

TREDGOLD ON THE STEAM ENGINE AND ON STEAM NA\aGATIO> 

\* This work having been selected as a Prize-book by the Institution of Civil Engineers, isd # - 
other Institutions, and by practical Engineers for presents to their Pupils, can be had in any <ftb£* ' 
of binding by giving seven days' notice. 



6. 

In 2 vols., very neatly half-bonnd in red morocco, gilt tops ; the Text in quarto, and the Plate? prc 

separately on tine Columbier folio paper, Price £7. 7«. 

TREDGOLD ON THE STEAM ENGINE AND ON STEAM NAVIGATION 



7. 

The Plates sold separately, on Columbier folio, very neatly half-bound in red morocco, gilt tops 

Price £5. 5«. 

TREDGOLD ON THE STEAM ENGINE AND ON STEAM NAVIGATIO 

\* In many instances purchasers of the work in 2 vols, have also possessed themselves ol '.i* 
Plates in a separate form, not only for practical use and reference, but as a Table-book, to exhi^ • 
splendour of the Steam Machinery of Britain. 



8. 

In quarto size, with four elaborately engraved Plates, and numerous Wood-cuts of Detafla, Priee £!■ ' 

in cloth boards. 

DESCRIPTION OF the PATENT LOCOMOTIVE STEAM ENGLV: 
OF Messrs. ROBERT STEPHENSON and Co., 

NBWCASTLS UPON TTNS. 

*4i* The above Work is affixed to the publication of the 2nd edition of Tredgold, and has been ps^ 
lished separately for the use of those who desire a perfect knowledge of the Locomotive Eeprl 
separate from other Steam Engines. The description is both popular and scientific, and was draws . I 
under the immediate superintendence of Robert Stephenson, Esq. The Engravings aire large,, and iM 
unique examples of mechanical engraving. The cost of the four Plates was £400 ; the «ood-<c*j 
40 in number, are explanatory of such details of the Engine as cannot be shown in the £levatir-| 
Plan, Cross or Transverse Section ; nor so well described in language as by the ocular demcNistntioB -fl 
these, intermixed as they are with the descriptive text. It will be found that this extraordinaiy mooe'i 
Engine, which owes its present improvements to the Stepbensons, is made available to tht i&illk»: 
being explained in the plainest language, and divested of mathematical foimulas, 

9. 
STEAM NAVIGATION. 

Just published, in Atlas folio size, uniform with Telford's works and the Atlas copies to Tred*oid. 

Price 12*. ® 

APPENDIX A, TO THE NEW EDITION of TREDGOLD ox ri:: 

STEAM ENGINE. 

CONTENTS. 

Plate I. — Iron Steam Yacht G^/ow^tPorm.constructed power each, 50>inch cylinders, 4-6 itiolce. m^ 

by John Laird, Esq., Birkenhead, Liverpool. by G. Forrester and Co., of Livetpod, and fin-> 

Plates II. and III. — Iron Steam Ship Hambowt on board of the Rainbow, 

belonging to the General Steam Navigation Plate V. — Side Elevation and Sectioii of ditta 

Ck>mpany, draught lines at bottom, fore body Plate VI. — ^Transverse Section of ditto, 

to a Urge scale, by Ditto. Plate VII. — Draught of the Americui Anr- 

Plate IV. — Plans of the Engines of QO-horse Steam Ship Fulion, Half the main brtra?:! 



W^' 



ARCHITECTURAL LIBRARY^ 59, HIQH HOLBORN. 



17 feet: distance between the water lines, 2 
feet ; fore and after body precisely alike. 
Plate VIII. — Plana of the Upper and Lower 
Decks of the Admiralty Yacht Firebrand^ 
showing the fittings and conveniences; drawn 



Plates IX. and X. — Plans of the Upper and Lower 
Decks of the Iron Steam Ship Nevkot con- 
structed for Her Imperial Majesty the Empress 
of Russia, by Messrs. Fairbaim and Murray, of 
Mill MTall, Poplar. 



by Mr. James Henry Lang, of Woolwich. 

APPENDIX B. is in preparation. To contain the remaining five Engravings of the Nevka, the 
Steam Engine in the Royal Arsenal at Woolwich, and other interesting subjects ; together with the Text 
for both Parts. Price 12«. 



10. 
Just published, vol. 3, with several Plates, Price £1, hi. 

PAPERS ON SUBJECTS CONNECTED WITH THE DUTIES OF 

THE CORPS OF ROYAL ENGINEERS. 

CONTENTS. 



Introclucilon. 

Memoranda relative to the Lines thrown up to 
cover Lisbon in 1810. By Colonel John T. 
JoNBS, Royal Engineers. 

Memoranda relating to the Defence of Cadiz, and 
explanatory details of the Position intrenched 
by the British troops under Lieutenant-General 
Graham, in 1810. 

Instructions of the Minister of War concerning 
the Model-towers approved of by Napoleon. 
Translated by Lieut. Laffan, Royal Engi- 
neers. 

Report on the Demolition of the Revetments of 
some of the Old Works at Sheemess, on Sa- 
turday the 14th July, 1827. 

Letter from Lieut.-Colonel Robert Thomson to 
Lieutenant Denison on the subject of Furnaces 
for heating Shot. 

Memoir on Posen, by T. R. Stavelt, Esq., late 
Captain Royal Engineers. 

Report on Beaufort Bridge. By R. J. Nelson, 
Lieutenant Royal Engineers. 

Rough Sketch of the Suspension Bridge over the 
Lalm at Nassau. By R. J. Nelson, Lieutenant 
Royal Engineers. 

Detailed Description of some of the Works on th^ 
Rideau Canal, and of the alterations and im- 
provements made therein since the opening of 
the navigation. By Lieutenant Denison, Royal 
Engineers. 

On the mode of Bending Timber adopted in 
Prussia. By R. J. Nelson, Lieutenant Royal 
Engineers. 

Description of the Coffer-dam used in the Con- 
struction of the Piers of the Alexandria Aque- 
duct, being an abstract of a report addressed 
by Captain Turnbull to Lieutenant-Colonel 
Abert, and by him submitted to the House of 
Representatives of the United States. 

Description of the one-arch Wooden-Bridge, of 



205 feet bpan, at Paradenia, with an account of 
the execution of the work and the me^ns em- 
ployed in throwing it across the river Malia^il- 
laganga, in the island of Ceylon. By Captain 
Oldershaw, Royal Engineers. 

Description of a Series of Bridges erected across 
the river Ottawa, connecting the provinces of 
Upper and Lower Canada, and especially of a 
wooden arch of 212 feet span which crossed 
the main branch of the river. By Lieutenant 
Denison, Royal Engineers. 

Description of a Barometer that requires no cor- 
rections either for Zero or for Temperature. 
By Samuel B. Howlett, Esq., Chief Draughts- 
man, Ordnance. 

Notes to aid in correcting the operation of ascer- 
taining the Heights of Mountains by means of 
Boiling W^ater ; furnished by Major Ord, Royal 
Engineers. 

On the Decomposition of Metallic Iron in Salt 
Water, and of its Reconstruction in a Mineral 
form. By Lieut.-Col. Reid, Royal Engineers. 

Report on the Effect of Climate on Yorkshire 
Paving, communicated by Colonel Fanshawk, 
Royal Engineers. 

Report of Paving Stables at Brighton. 

Experiments tried at Quebec as to the properties 
and adhesive qualities of Cements, by order of 
Colonel NicoLLS, Commanding Royal Engineer, 
dated 17th November, 1834. 

Proof of an Earthen Ware Pipe for Lieutenant 
Denison. By Mr. Bramah. 

Description of a Drawbridge on the London and 
Birmingham Railway, at Weedon. By Captain 
J ebb, Royal Engineers. 

Table of the Description and Weight of the 
Packages of various Articles of Traffic. By 
Majo^ H. D. Jones, Royal Engineen. 

Appendix. — Notes on Lintz. 

Notes to pages 36 and 39. 



11. 

VoL 2, uniform vrith the preceding, Price £1. 



12. 
Vol. 1, reprinting, Price 15#. 



^ 



-® 




13. 
1&3 Plates, engraved in the bett ttyle of Ait, half-bonnd, very neat, Price iE4. 4i. 

PUBLIC WORKS OF GREAT BRITAIN ; 

CONSISTING OF 

Railways, Rails, Chairs, Blocks, Cottings, Embankments, Tunnels, Oblique Arches, Viadncli, Bn^ 
Stations, Locomotive Engines, &c. ; Cast-Iron Bridges, Iron and Gas Works, Canab, Lod-cs& 
Centering, Masonry and Brickwork for Canal Tunnels ; Canal Boats ; the London and livenncllt^. 
Plans and Dimensions, Dock-gates, Walls, Quays, and their Masonry; Moorlng-cbains, PIib «^ 
Harbour and Port of London, and other important Engineering Works, with DescripCioos ssd S^- 
cations ; the whole rendered of the utmost utility to the Civil Engineer and to the Nobility i^ Gtsr 
as Monuments of the useful Arts in this Country, and as Examples to the Foreign Eng;ijieei. 

Edited bt F. W. SIMMS, C. E. 

This Work is on an Imperial folio size, the Drawings and Engravings have been executed bj esiae 
Artists, and no expense has been spared in rendering it highly essential to the Ctvil En^acff ■ 
Studq;it ; also, as an ornamental Volume of Practical Representations of important Engineennf ^^* 
in several Parts of the Kingdom. The Work is bound in half-morocco, there aie some Pistes a^^ 
Volume that may be prefeired in Colours, viz., the elaborate subject of the Blisworth Cuttia|s,is' 
Birmingham Line, 18 Plates, geologically coloured ; Glasgow and Gaimkirk Raflway Cuttiog tkmr 
Moss, geologically coloured, &c. ; making 20 Plates, to be carefully coloured, and for w^ ^ 
additional £1. It, is charged. 

The following UalUt qfthe Authort whose worke are conqfrieed m the 



Brindley 

Brunei 

Buck 

G. and R. Stephenson 



Hartley 
Hosking 
Jessop 
Landmann 



M'Adam 
Palmer 
Rennie 
Rhodes 



Telford 
Thomas 
TieraeyCliA 
Walker. 



14. 
22 Plates, large folio, bound. Price £1. U, 

THE HARBOUR AND PORT OF LONDON, 

SCIKMTIFICALLY, COMMB&CIALLT, AND HISTORICALLY DX8CRIBBD ; 

Containing Accounts of the History, Privileges, Functions, and Government thereof; of its S^* 
Divisions, and Jurisdictions, Municipal and Commerdal; of its Docks, Piers, Quays, EmbsnbBa*'* 
Moorings, and other Engineering Works ; Tidal and other Observations, and every other nectssfj 
information relative thereto, accoqipanied by Charts of the Port and its Dependencies, its Sboiis ^ 
Soundings, surveyed by order of the Port of London Improvement Committee ; Plans of Docici> Gik^ 
Piers, Swivel Bridges, Methods of Mooring Vessels, &c., as directed by the Corporation Br-U*^ 
&c., &c., &c. 

By JAMES ELMES, Architect and CivQ Engineer, Surveyor of the Port of Loadoa. 



15. 
In 8vo., with Engravings and Wood-cuts, cloth bds. extra, Price 12a. 

OUTLINE OP THE METHOD OF CONDUCTING A 
TRIGONOMETRICAL SURVEY, 

For the Formation of Topogr^>hical Plans ; and Instructions for Filling-in the Interior DetaQ, ^^ • 
Measurement and Sketching { Military Reconnaissance, LeveUing, &c., &c ; 

With the Explanation and Solution of some of the most nseAil Problems in Geodesy and Tne^ 
Astronomy ; to which are added, a few Formule and Tables of general utility for £idlitatiog 

their calculation. 

By Lieutenant FROME, Rotal Enoinbsrb, F.R.A.S., & A.I.C.B. 



ARCHITECTURAL LIBRARY, 59, HIGH HOLBORN. 



7 



16. 
RAILWAYS. 

In Imperial folio, 83 Engravings, with eiplanatory Text, containing the Specification of the Works as 

executed. 

Edited by F. W. SIMMS, C.E. 

Price £2. I2i, 6d. in half-morocco. — Subjects : 

Thb London and Birmingham Railway — ^Thb Giusat Western Railway — The South- 
ampton Railway — The Greenwich Railway — The Croydon Railway — The Birmingham 
and Bristol Thames Jdnction Railway — Glasgow and Gairnkirk Railway. In 83 Plates, 
with Sections, Details, &c. 



LONDON AND BIRMINGHAM RAILWAY. 



1. 

2. 
3. 
4. 

6. 
6. 

7. 
8. 

9. 
10. 

11. 

13. 

13. 
14. 
15. 
16. 
17. 



Frontiapiece— London Entfaaee to the PrimroM HOI 
Tunnel. 

Tide Fttge, rignette— Railwar SUtion at Watford. 
Chimney* at Camden Town fixed Engine Station. 
Entnuice to Railway Station at Euston Grore — Vig- 
nette, page I. 

Enaton Grave Station, ground-plan* 
Camden Town fixed Engine Station, ground-plan. 
Iron Roof— Euston Grore Station. 
Stanhope Place and Park Street Bridges. 
Brid^ orer the Regent** Canal. 
Detail* of ditto. 

London and Birmingham Railway — Harrow in the 
distance. Vignette, page 17. 

London and Birmingham Railway—- Watford Tunnel. 
Vignette, page S8. 
Road Bridge over Railway. 
Colne Viaottct. • 

Bridge over Excavation south of Watford Tunnel. 
Box Moor Oblique Brid^. 

North Chnrdi and Primrose Hill Tunnels — Cross 
Secti<ms. 



18, I9< Entrances to ditto— Vignettes, pages SI and 84. 

SO to SO' Working Section, Bliswortn Kxcavations and 
Embankments. 

SO, 81. Undersetting of Rock in Blisworth Cuttings — ^En- 
larged Scale. 

SS, S3. Plan and Elevation of Retaining Walls, Counter- 
forts, Inverts, Drains, &c. in the Blisworth Cuttings. 

34, 35. General Plan and Section of the Undersetting of 
the Rock in the Blisworth Cuttings. 

30, 37. Plan, Elevation, and Section of the West End of 
the Blisworth Cuttings. 

38 to. 47. Plan, Elevations, and Details of the Kflsby Tun- 
nel, Warwickshire. 

48. Method of fixing the Fifty-pound Rails in the 
Chairs. 

49. Method of fixing the Sixty-five-pound Rails in the 
Chairs. 

60. Mr. Buck's Railway Chairs. 

61. Plan (rf Siding or Passing Place. 

62. Plans and Sections of a 'IVelve-feet Turn Rail. 

63. Plan and Elevation of First Class Carriages. 



GREAT WXBTBRN RAILWAY. 



54. Plan and Elevation of the Brent l^aduet. 

55. Sections of the Brent Viaduct. 

&6. Transverse Sections of the Brent Viaduct. 



57. Plan and Elevation of Maidenhead Bridge. 

58. Sections of Maidenhead Bridge. 

69. Occupation Bridge over the Bulway. 



SOUTHAMPTON RAILWAY. 



60. Bridge under Railway. 

61. Plan of ditto. 

62. Occupation Bridge in Embankment. 



65. Oblique Arch over Neekinger Road. 

Od. Sections of ditto. 

67. OUiqne Arch over Spa Road. 



71. New Cross Bridge over Railway. 



63. Occupation Bridge. 

64. Elevation and Details of Earth-work and Timber 
Waggons. 



GREENWICH RAILWAY. 



08, 09. Sections of ditto. 

70. Viaduct of the Greenwich Railway. 



CROYDON RAILWAY. 

72. Method of fixing the Permanent Way. 



BIRMINGHAM AND BRISTOL THAMES JUNCTION RAILWAY. 

73. Cast-iron Arch Suspension Bridge over the Paddington 74. Railway Gallery under the Canal, &c. 
Canal and the Railway. 

GLASGOW AND GAIRNKIRK RAILWAY. 
76. Transverse Section at Robroyston Moss. 

MISCBLLANBOU8. 



i 



7O. Comparison of the Transverse Section of numerous 
Railway Bars. 

77. Comet Locomotive Engine. 

78. Mr. Stephenson's Patent Locomotive Engine. 

79. Railway Waggons. 



80. Flat Rail with Flange. 

81. Rail by Losh, Wilson, and BeU. 
89. HettonRail. 

83. Sidings or Passing Places. 



® 



8 



WORKS PUBLISHED BY JOHN WBALE^ 



17. 

fS^t JlrfD Wiatk an SrOrge Sufllrinf. 



Vol. 1, royal octavo, is just completed, Price £1. ]6«., containing 380 pages of Text and 55 elaborately 
engraved Plates, with every detail and dimension for practical use, entitled, 

THEORY, PRACTICE, AND ARCHITECTURE OF BRIDGES. 

The theory by JAMES HANN, of Kino's College, 

Hon. Mem. of the Philosophical Society of Newcastle upon Tyne, Mem. of the MathematicaL Sodety 

of London, and Joint Author of " Mechanics for Practical Men ;*' 

AMD 

The practical ENGINEERING and ARCHITECTURAL TREATISE 

BY WILLIAM HOSKING. F.S.A., 
Architect and Civil Engineer, Author of ** Treatises on Architecture and Bofldiiig ;'' 

PROFESSOR MOSELEY, M.A., Kino's College ; T. HUGHES, and ROBERT STEVENSON, 

Civil Engineers. 

The Work will be completed in 2 Vols., to contain 700 pages of Text, and illustrated by 110 En- 
gravings of examples of Stone, Timber, Iron, Wire, and Suspension Bridges, from Drawings furnished 
by the principal Engineers of Great Britain and France. 

Vol. 2 is preparing, and is to be published in 6 Parts, at intervals, in the course of the year 1840. 

\* This Work, when completed, vriU be found to be of a roost valuable character, the highest takat 
having been engaged for the Engravings, and the price made convenient to the Student. 

AtloM cqpiet qfthe Plate§ may be had. 



18. 
In demy 8vo., nnmerous Wood-cuts, extra cloth bds., Price 8». 

AN ESSAY ON THE BOILERS OF STEAM ENGINES: 

Their Calculation, Construction, and Management, with a view to the saving op fukl. Indnding 
Observations on Railway and other Locomotive Engines, Steam Navigation, Smoke Burning, Incrus- 
tations, Explosions, &c. &c. A New Edition, considerably enlarged and improved. 

By R. ARMSTRONG, CivU Engineer. 



19. 

Vol. 1, Price 30«., extra doth bds., containing a Portrait of the Ute President, Thos. TeUbrd, Esq., 

and 27 finely engraved Plates. 

transactions of the institution of ci\aL 

engineers. 

%* Except 15 copies, which only remain of this Volume, all of them being defident of Mr. Macneill's 
Tables, the Volume is out of print, and scarce. It will however be reprinted some time in the year 
1840. 



20. 
Vol. 2, Price 28«., extra cloth bds., containing 23 findy engraved Platea. 

TRANSACTIONS OF THE INSTITUTION OF CIVIL 

ENGINEERS. 

LIST OF SUBJECTS. 



Account of the Bridge over the Severn, near the 
Town of Tewkesbuiy, in the County of Glou- 
cester, designed by Thomas Tklford, and 
erected under his su|>erintendence. By W. 
Mackenzie, M.Inst.C.E. 



-^i* 



A Series of Experimenta on diffbcnt kinds of 
Amaican Timber. By W. Dbnibon, Ueiit 

Royal Engineers, F.R.S., A.Inst.C.£. 
On the Application of Steam as a moving Power. 
considered especially with tefereaoe to thf 



t 



ARCHITECTURAL LIBRARY, 59, HIGH HOLBORN. 



® 



economy of Atmospheric and High Pressure 
Steam. By Gsorob Hol worthy Palmer, 
M.Inst.C.E. 

Description of Mr. Henry Gay's method of giTing 
a true Spherical Figure to Balls of Metal, Glass, 
Agate, or hard Substances. Communicated by 
Brtan Donkin, V.P.ln8t.C.£. 

On the expansive action of Steam in some of the 
Pumping Engines on the Cornish Mines. By 
William Jort Hemwood, F.G.S., Secretary 
of the Royal Geological Society of Cornwall, 
H. M. Assay-Master of Tin in the Duchy of 
Cornwall. 

On the effective power of the High Pressure ex- 
pansive condensing Engines in use at some of 
the Cornish Mines. By Thomas Wickstkbd, 
M.Inst.C.E. A letter to the President. 

Description of the Drops used by the Stanhope 
and Tyne Railroad Company, for the Shipment 
of Coals at South Shields. By Thomas £. 
Harrison, M.Inst.C.E. 

On the Principle and Construction of Railways of 
continuous bearings. By John Rbynolds, 
A.Inst.C.E. 

Wooden Bridge over the River Calder, at Mh^eld, 
Yorkshire, designed and erected by William 
Bull, A.Inst.C.£. 

A Series of Experiments on the Strength of Cast 
Iron. By Francis Bramah, M.Iiist.C.£. 



On certain Forms of Locomotive Engines. By 
Edward Woods. 

Account and Description of Youghal Bridge, de- 
signed by Alexander Nimmo. By John £. 
Jones, AIiist.C.£. 

On the Evaporation of Water from Steam Boilers. 
By JosiAH Parkss, M.Iiist.C.£. 

Account of a Machine for cleaning and deepening 
small Rivers, in use on the Little Stour River, 
Kent. By W. B. Hats, GTad.Inat.C.E. 

Description of the Perpendicular Lifts for passing 
Boats from one Level of Canal to another} as 
erected on the Grand Western CanaL By 
James Green, M.In8t.C.£. 

On the methods of Illuminating Lighthouses, wiih 
a description of a Reciprocating light. By J. 
T. Smith, Captain Madras Engineen, F.R.S., 
A.In8t.C.E. 

Experiments on the Flow of Water through small 
Pipes. By W. A. Provis, M.In8t.C.E. 

Experiments on the Power of Men. By Joshua 
Field, V.P.Inst.C.E., F.R.S. 

Particulars of the Construction of the Floating 
Bridge lately established across the Hamoaze, 
between Torpoint in the County of Cornwall, 
and Devonport in Devonshire. By Jakes M. 
Rendel, M.Inst.C.E., &c. &c. 

Appendix. — Officers, Members, &c. 



21. 
Vol. 3, Part L, extra doth boards, Price is, 

TRANSACTIONS OF THE INSTITUTION OF CIVIL 

ENGINEERS. 

CONTBNTB. 

On Steam Boilers, by Josiah Parkbs, M.In8t.C.E. 



22. 

VoL 3, Part IL 

TRANSACTIONS OF THE INSTITUTION OF CIVIL 

ENGINEERS. 

CONTENTS. 



On Steam Boilers and Steam Engines, Part. II. 
By JosiAH Parses, M.In8t.C.E. 

On the Comparison between the Powa of Loco- 
motive Engines and the Effect produced by 
that Power at different Velocities. By Pro- 
fessor Barlow, Hon. M.Inst.C.E. 

On the Properties, Uses, and Application of Turf, 
Tuif-Coke, and Resin PueL By C. Wye Wil- 
liams, A.Inst.C.£. 

Description of a Sawing Machine for cutting off 
Railway Bars. By Joseph Gltnn, M.In8t.C.E. 
1 Plate. 

On the State of the Suspension Bridge at Mon- 
tiose after the hurricane of the 11th of October, 
1838, with Remarks on the Construction of 



that and other Suspension Bridges, in reference 
to the action of violent gales. By C. W. Pas- 
let, Colonel R.£., Hon. M.Inst.C.E. 1 Plate. 

On the Expansion of Iron and Stone in Structures, 
as shown by observation on the Southwark and 
Staines Bridges. By George Rennie, F.R.S., 
&c. &c. 

The Gravesend Pier. By W. Tiernbt Clark, 
M.Inst.C.£. 6 Plates. 

On Well-sinking near the Metropolis, with an 
account of the Well sunk by the New River 
Company at their Reservoir in the Hampstead 
Road. By R. W. Mylne. 1 Plate. 

On Locomotive Engines. By Edward Bury, 
M.ln8t.C.E. 4 Plates. 



^ 



10 WORKS PUBLISHED ^Y JOHN WEALE, 



23. 
In Svo., Price 8«. 

A PRACTICAL TREATISE ON THE CONSTRUCTION AND 

FORMATION OF RAILWAYS, 

Showing the Practical Application and Expense of Excavating, Haulage, Embankingi and permanent 
Waylaying ; also, the method of fixing Roads upon continuous Timber Bearings ; including the pric- 
ciples of Estimating the Gross Load and Useful Effect produced by Mechanical or other MotiTe Pover, 
upon a Level and upon any Inclination. Illustrated with Diagrams and Original Useful Tables. 

By JAMES DAY. 



24. 
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THE RAILWAY CALCULATOR, OR ENGINEER'S AND 

CONTRACTOR'S ASSISTANT- 

By JAMES DAY. 



25. 
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TABLE SHOWING THE CONTENTS OF EXCAVATIONS, 

Intended to facilitate the Estimating of Public Works. 
By GEORGE P. BIDDER, CJB. 



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A PRACTICAL AND THEORETICAL ESSAY ON OBLIQUE 

BRIDGES. 

By GEORGE WATSON BUCK, M.Inst.C.E. 



27. 
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A PRACTICAL TREATISE ON THE CONSTRUCTION OF 

OBLIQUE ARCHES. 

By JAMES HART, Mason. 



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EXPERIMENTAL ESSAYS ON THE PRINCIPLES OF CON 
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Made with a view to their being useful to the Practical Builder. 
By W. BLAND, Esq., of HarUip, Kent. 



29. 
In royal 8vo., in boards, with nine Charts and one Meteorological Table, Price £1. It. 

AN ATTEMPT TO DEVELOP THE LAW OF STORMS, 

By means of Facts arranged according to Place and Time ; and hence to point out a Cause for iht 
VARIABLE WINDS, with the view to practical usb in nayigation. 

By lieut-Colonel W. REID, C.B., of the Royal Engineers. 
Some copies with the Charts in a separate Atlas form. Price £1. &«. 

# ^ 



3> 



ARCHITECTURAL. LIBRARY^ 59^ HIGH HOLBORN. 11 

30. 
In demy 8¥0.r extn cloth boards. A New Work, Price 12«. 

THE THEORY OF THE STEAM ENGINE; 

Showing the Inaccuracy of the Methods in use for calculating the Effects or the Proportions of 
Steam Engines, and supplying a Series of Practical Formnle to determine the Velocity of any Engine 
with a given Load, the lioad for a stated Velocity, the Evaporation for desired Effects, the Horse- 
power, the useful Effect for a given Consumption of Water or Fuel, the Load, Expansion, and Counter- 
weight fit for the Production of the Maximum useful Effect, &c, with 

AN APPENDIX, 

Containing concise Rules for persons not familiar with Algebraic Signs, and intended to render the use 

of the Formulae contained in the work perfectly clear and easy. 

By COMTE DE PAMBOUR, 
Formeriy a Student in the E'oole POlytechnique, late of the Royal Artillery, on the Staff in the French 

Service, of the Royal Order of the I>%ion d'Honneur, &c. 



31. 
In 8vo., cloth, Price '2s. M. 

A NEW SYSTEM OP SCALES OF EQUAL PARTS, 

Applicable to various purposes of Engineering, Architectural and General Science. Illustrated by a 

Facsimile of the Scales on Copper-plate. 

By CHARLES HOLTZAPFFEL, Assodste of the Institution of Civil Engineers. 



32. 

In demy 8vo., extra cloth boards, with 16 Plates, Price 12s. 

A SKETCH OF THE CIVIL ENGINEERING OF NORTH 

AMERICA. 

Comprising Remarks on the Harbours, River and Lake Navigation, Lighthouses, Steam Navigation 
Water-works, Canals, Roads, Railways, Bridges, and other works in that country. 

By DAVID STEVENSON, of Edinburgh, CivU Engineer. 



33. 
COLONEL PASLEY'S COMPREHENSIVE WORK ON GEOMETRY. 

Second Edition, demy Svo., much enlarged, Price 16«. cloth boards, (instead of £1. 4s.), 

A COMPLETE COURSE OF PRACTICAL GEOMETRY AND 

PLAN DRAWING J 

Treated on a principle of peculiar Perspicuity. Adapted either for Classes, or for Self-Instruction. 
Originally published as the first volume of a Course of Military Instruction. 

By C. W. PASLBY, C.B., Colonel Royal Engineen, F.R.S., &c &c 



34. 
In demy Svo., extra doth boards, numerous Wood-cuts, Prioe 14s. 

OBSERVATIONS ON LIMES, CALCAREOUS CEMENTS, 
MORTARS, STUCCOS, AND CONCRETE, 

AND ON PUZZOLANAB, NATURAL AND ARTIFICIAL; TOOBTHBR WITH RULXS DBDUCBD 
rROM NVMBROUB XXPXRIMBNT8 FOR MAKING AN ARTIFICIAL WATBR CBMBNT, 

Equal in Efficiency to the best Natural Cements of England, improperly termed Roman Cements ; and 

an Abstract of the Opinions of former Authors on the want Subjects. 

By C. W. PASLEY, C.B., Colonel in the Coips of Royal Bn^^eers, r.ltS., &c. &c. &c 
t 



12 WORKS PUBLISHED BY JOHN WEALIS, 

35. 

Second Edition, with Additional Corrections, in 8vo., with a fine Frontispiece of a Locomotive Enpat. 

Price St. 

ANALYSIS OF RAILWAYS; 

Consisting of Reports of Railways projected in England and Wales ; to which are added, a Tabk d 
Distances from the proposed London Terminus to Eight well-knovm Places in the Metropolis, with i 
copious Glossary, and sereral Useful Tables. 

By FRANCIS WllISHAW, C.E., M.InstX.E. 



36. 
Just published, in 8to., bound, Price 3«. 6d. 

THE PRACTICE OF MAKING AND REPAIRING ROADS ; 

OF CONSTRUCTING FOOTPATHS, FENCING, AND DRAINS ; 

Also a Method of comparing Roads with reference to the Power of Draught required : with Praciki 
Observations, intended to simplify the mode of Estimating Earth-work in Cuttings and Embankme&ti. 

By THOMAS HUGHES, Esq., CivU Engineer. 



37. 
With folding Plates, in 4to., Price 3«. 

SECTIO-PLANOGRAPHY; 

A DESCRIPTION OF MR. MACNSILL's METHOD OF LAYING DOWN RAILWAY 8XCT10NS 

AND PLANS IN JUXTAPOSITION. 

As adopted by the Standing Order Committee of the House of Commons, 1837. 

By FRED. W. SIMMS, Civil Engineer. 



38. 

In 8vo., with several Plates, Price 16«. 

A TREATISE ON THE STRENGTH OF TIMBER, CAST IRON, 
MALLEABLE IRON, AND OTHER MATERIALS, 

With Rules for Application in Architecture, Construction of Suspension Bridges, Railways, &c. ; wit^ 
an Appendix on the Powers of Locomotive Engines on Horizontal Planes and Gradinits. 

By PETER BARLOW, F.R.S., &c &c. 



39. 

Third Edition, with 28 additional Plates, Edited by Peter Barlow, Esq., F.R.S., M.LC.E., in extn 

half-morocco. Price £2. 2t, 

ELEMENTARY PRINCIPLES OF CARPENTRY, AND ON 

CONSTRUCTION. 

A Treatise on the Pressure and Equilibrium of Beams and Timber Frames, the Resistance of Timbers 
and the Construction of Floors, Roofs, Centres, Bridges, &c. ; with Practical Rules and Examples. T 
which is added, an Essay on the Nature and Properties of Timber; including the Methods of Seasonirc 
and the Causes and Prevention of Decay ; with Descriptions of the Kinds of Wood used in Building 
also numerous Tables of Scantlings of Timber for different purposes, the Specific Gravitiea of Materials 
&c. Illustrated by 50 Engravings. 

By THOMAS TREDGOLD, avfl Engineer. 



ARCHITECTURAL LIBRARY, 59, HIGH HOLBORN. 13 

40. 
In Quarto, 28 fine Plates, Price £1. U, 

TREDGOLD'S ELEMENTARY PRINCIPLES OF CARPENTRY, 

AND ON CONSTRUCTION. 

SUPPLEMENT TO THE SECOND EDITION. 

Sold separately for the convenience of those possessing the former Edition. 

Comprising Engravings of Iron and Timber Roofs of Italian Palaces, Churches, Theatres, &c. ; of a 
Juvenile Prison, Pantheon Bazaar, &c. &c., by Mr. Sydney Smirks ; Iron and Timber Roof, &c. of 
Christ's Hospit^ and St. Dunstan's in the West, by Mr. John Smaw ; Timber Roofs of White Conduit 
House Tavern and others, by Mr. Duncan ; Iron and Timber Construction of Croydon Railway Station, 
by Mr. Jos. Gibbs ; Iron and Timber Roofs of the Trent Water- works, Nottingham, and the Roofs of 
the Model Room, the Smithery, and Engine Manufactory, at Bntterley, by Mr. Jos. Glynn ; with Mr. 
Mackenzib's elaborate Drawings of the Construction of King's College Chapel, Cambridge. The 
whole described by the different Contributors, and edited by Peter Barlow, Esq., F.R.S., &c. &c. 



41. 
Royal 8vo., Price 7«. 6d. 

AN ESSAY ON THE MODERN SYSTEM OF FORTIFICATION 

Adopted on the Rhine and Danube, and followed in all the works constructed since the Peace of 1815, 
in Germany. Illustrated by a copious Memoir on the Fortress of Coblentz, and accompanied by 
beautiful Plans and Sections of the works of that place. 

By Lieutenant-Colonel J. H. HUMFREY, K.S.F., 

Formerly of the Royal Artillery and Royal Staff Corps, and late Commanding Engineer to the Corps of 
Cantabria, Author of several Military Works, &c. Long resident in Germany, where he had oppor- 
tunities of collecting information firom the best sources. 



42. 
In 8vo., upwards of 500 pages,- Price St, 

AN ELEMENTARY INVESTIGATION OF THE THEORY OF 

NUMBERS, 

With its Application to the Indeterminate and Diophantine Analysis, the Analytical and Geometrical 
Division of the Circle, and several other carious Algebraical and Arithmetical Problema. 

By PETER BARLOW, Esq., F.R.S., M.In8t.C.£., and of several other Learned Societies and Academies. 



43. 
With Plates, 8vo., Price 6*. 

A PRACTICAL TREATISE ON THE PRINCIPLES AND PRACTICE 

OF THE ART OF LEVELLING, 

With Practical Elucidations and Illustrations, and Rules for Making Roads upon the principle of 
Tblfo&d ; together with Mr. Macnbill's Instrument for the Estimating of Roads, &c. 

A work most essential to the Student 



44. 
Engraved in aquatinta and coloured, 38 Plates. Quarto. Price £1. As. 

ARCHITECTURAL SKETCHES FOR COTTAGES, RURAL 

DWELLINGS, AND VILLAS; 

With Plans, suitable to persons of genteel life and moderate fortune, prop^ ^^^ Picturesque BuUdings. 

By R. LUGAR, Architect ' ^ 

® 



14 



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45. 

Lai^ Atlas folio, 17 very findy engiraved Plates, Price JC4. 14*. 6dl — ^A few copies only of 

India paper, Price £6. 6t. 



a 



SUSPENSION BRIDGES. 

A SCIENTIFIC and an HISTORICAL and DESCRIPTIVE ACCOUNT of the SUSPENSIOV 
BRIDGE constructed over the MENAI STRAIT, in North Wales; with a brief Notice of CONW.4T 
BRIDGE. From Desig:ns by and under the direction of Thomas Tblfokd, F.R.S., L. and E^ &c. Al- 
and Albxander Provis, Esq., Resident Eng;ineer. 



46. 
In 8vo., with Plates, Price 12f. 

CEMENTS. 

A PRACTICAL and SCIENTIFIC TREATISE on the Choice and Preparation of the Materials lor, ati 
the Manufacture and Application of, Calcareous Mortars and Cements, Artificial and Natural, fbosd*^ 
on an Extensive Series of Original Experiments. By M. L. J. Vicat, Chief Engineer of Roads, tz 
Translated firom the French, with numerous and valuable Additions, and Explanatory Notes, am.- 
prehending the most important known Facts in this Science, and with additional new Experiments at-- 
Remarks. 

By Captain J. T. SMITH, Madras Engmeers. 



47. 
In 12mo., Price 2«. 6 J. in boards. 

RULES AND DATA FOR THE STEAM ENGINE, 

BOTH STATIONARY AND LOCOMOTIVE ; 

And for railways, canals, and turnpikb roads : being a Synopsis of a Course of Eight Lectiar 
on MBCHANicAL PHILOSOPHY ; illustntive of the most recent modes of Construction, and an Expoatw: 
of the Errors to which Patentees and others are liable, from their not being acquainted with ik 
practical departments of Engineering. 

By HENRY ADCOCK, CiyU Engineer. 



48. 

In 5 Parts, large oblong folio, with a Letter-press Description in 4to. to each. Price £1. Is. eecfa Put. 

with the Text. 

THE CIVIL ENGINEER AND MACHINIST: 

PRACTICAL TREATISES OF CIVIL ENOINBBRING, BNGINEBR BUILDING, MACHINBET. 
MILL-WORK, BNGINB-WORK, IRON-FOUNDING, &C. &C. 

By C. J. BLUNT. 

CONTENTS. 



«• 



Division 1. — Bonlton and Watt's Portable ^team 
Engine, complete, with all the details, in 10 
Plates. 

Division 2. — Marine Steam Engines and Ma- 
chinery; Steam Com Mills, &c., complete. 

Division 3. — Sugar Mills, on horizontal and verti- 
cal construction ; Steam Com Mills, by Mauds- 
LAT and FiKLD ; the Kent and Surrey Sewers, 
Sluices, &c; Smith's Forge, and Great Forge 
Hammer. 

Division A. — Sea Entrance Gates, Swing Bridges, 
Canal Bridge, Specifications of the Works, &e^ 
of the Gloucester and Berkeley Canal, Water- 



wheels and Iron Rooft, by the late Troma* 
Telpord ; Plans, Sections, and Machinery of t>' 
Wemyss Colliery, &c 
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original Specifications of the London and Bcr- 
mingham Railway, Locomotive and Bogie Es- 
gines of do. in detail, the Goods Waggaa5 
Tenders, and divers Specifications of Worici 
&c. &c., by RoBBRT Stephsnson, Esq. ; L£m>v 
motive Engines on the Newcastle and Cari]>- 
Railway, by Gsorgb Stephenson, Esq. ; tU 
Great Western Railway Bridge, &&, by J. k 
Brunbl, F.R.S., &c. &c 



9 



^ -^ ■ 

ARCHITECTURAL LIBRARY, 59, HIGH HOLBORN. 15 



49. 
Five Lmaisonf. Plates Atlas fblio» with Text in 4to. 

LOCOMOTIVE ENGINBS AND CARRIAGES. 

POPULAR FRENCH WORK. 

L'Industkib dks Chsmins db Fbr, ou Dessins et Descriptions des Machines Locomotives, des Four- 
gons d'approTisionnement (Tenders), Wagons de Transport et de Terrassements, Voitures, Diligences, 
lUdls, Supports, Plates-Formes mobiles. Aiguilles, Machines accessoires, &c. &c., en usage sur les 
Routes en Fer, de France, Angleterre, Allemagne, Belgique, &c. &c 

Par MM. ARMENGAUD. 



50. 
Second Edition, in 8vo, extra cloth boards, 10 Plates, Price 7«. 6J. 

PERSPECTIVE SIMPLIFIED; 

Containing a new frkliminart CHApraR, in which the subject is treated in the most plain and easy 

manner, for the convenience of readers not acquainted with Geometry. 

By Z. LAURENCE, Esq. 



51. 
In 4to., with Wood-cuts, and 4 fine Engravings by John Lb Kbvx, Price 7t. M. 

AN ACCOUNT OP THE ROOF OF KING'S COLLEGE CHAPEL, 

CAMBRIDGE. 

By F. MACKENZIE, Author and Draughtsman of some of the finest Architectural Works. 



52. 

In demy 8vo., 3 Engravings, Price 7«. 6<l. 

MECHANICS FOR PRACTICAL MEN; 

Containing Explanations of the Principles of Mechanics ; the Steam Engine, with its varions Pro- 
portions; Parallel Motion, &c. ; Tables of the Weight of Cast-iron Pipes, Strength and Stress of 
Materials, &c. 

By JAMES HANN, King's College, and ISAAC DODDS, C.E. 



53. 
4to., Price £\» If. Rerised and corrected. 

THE CARPENTER AND JOINER'S ASSISTANT; 

Containing Practical Roles for making all kinds of Joints, and yarioos methods of hingeing them 
together ; for hanging of Doors ; for fitting up Windows and Shutters ; for the construction of Floors, 
Partitions, Soffits, Groins, Arches for Masonry ; for constructing Roofs in the hest manner from a given 
quantity of Timher, &c. Also Extracts from M. Belidor, M. du Hamel, M. de Buffon, &c., on the 
Strength of Timher. Illustrated with 79 Plates. 

By PETER NICHOLSON, Architect. 



54. 
In 8to., with two large folding Plates of Sections of Roads, Price 2s. 

MAKING AND REPAIRING ROADS. 

RULES for MAKING and REPAIRING ROADS, as laid down by the late Thomas Tklfoao, Esq., 
Civil Engineer. Extracted, with additions, from a Treatise on the Principles and Practice of Levelling. 

By F. W. SIMMS, Surveyor and Ci'v\^ Engi^^^- 



16 



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55. 
4to., with Plates. Price 15t. 

A TREATISE ON RIVERS AND TORRENTS, 

With the METHOD of REGULATING their COURSE and CHANNELS. By Paul Fmsi, Member 
of numerous Academies. To which is added, an ESSAY on NAVIGABLE CANALS, by the same. 

Translated by Major-General JOHN GARSTIN. 



56. 

Wood*cut8, 8vo. Price 5». 

SECOND REPORT ON THE LONDON AND BIRMINGHAM 

RAILWAY, 

Foonded on an Inspection of, and Experiments made on, the LiTerpool and Manchester Railway. 

By PETER BARLOW, F.R.S., &c. &c 



57. 
Wood-cuts, 8vo. Price 4t. 6d. 

AN ESSAY ON THE CONSTRUCTION' OF THE FIVE ARCHl 
TECTURAL SECTIONS OF CAST-IRON BEAMS, 

Employed as Girdersi Bressummers, and other Horizontal Si^ports for Buildings, &e. 

By WILLIAM TURNBULL. 



58. 
Third Edition. Folio, urith a hirge Athis of Plates. Price £4. 4a. 

NAVAL ARCHITECTURE; 

Or, the RUDIMENTS and RULES of SHIP BUILDING .- exemplified in a SERIES of DRAUGim 
and PLANS ; with Observations tending to the further Improvement of that important Ait. Dedicated 
by penniasion, to His late Majesty. 

By MARMADUKE STALKARTT, Naval Architect. 



59. 
Three vols, large 4to., numerous fine Plates. Price £3. 3«. 

HISTORY OF MARINE ARCHITECTURE. 

By JAMES CHARNOCK, F.S.A. 

Illustrative of the Naval Architecture of aU Nations from the eariiest period, particulariy British. 

\* Chamock is a work essential to all who study the construction of ships, large and small aJ^ 

whether for war, packet, or mercantile purposes. 



60. 
Supplementary and Fifth Volume to the Antiquities of Athena, by R C. Cockerell, Esq., &c. 

ANTIQUITIES OF ATHENS AND OTHER PLACES OF GREECE, 

SICILY, &c. 

Supplementary to the Antiquities in Athens, by JAMES STUART, F.RS.. F.S.A., and NICHOLV^ 
REVETT; delineated and illustrated by R. C. Cockkrell, RA., F.S.A., W. Kinnard, T. L. DoAir 
SON, Member of the Institute of Paris, W. Jenkins, and W. Railton, Architects. 

Imperial folio, uniform with the Original Edition of Stuart and Revett, and the Dilettanti Wcri^ 
Very finely printed, and with numerous beautiful Plates of Plans, Elevations, Sections, Views, Ore-- 
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ARCHITECTURAL LIBRARY^ 59^ HIGH HOLBORN. 



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61. 

Very neatly half-bound in morocco, gilt tops, Price £3. 3». 

ARCHITECTURE OF THE METROPOLIS. 

DKOICATKD TO lYDNBT SMIEKB, »«., AECHITKCT, V.B.A., V.G.B. 

A New and Considerably Enlarged Edition, with many Additional Subjects and Plates, of 

ILLUSTRATIONS OF THE PUBLIC BUILDINGS OF LONDON, 

In Two Volumes 8vo., with 165 Engravings, origplnally edited by the late Augustus Pugin, Arcliitect, 

and John Britton, F.S.A., &c., and now newly Edited and Enlarged 

By W. H. LEEDS. 



Manifold as are the publications which represent 
the various structures of the metropolis, this is 
the only work which describes them, not ad libi- 
tuntf in views which, even when perfectly correct, 
show no more than the general aspect and locality 
of each building from a certain point, and conse- 
quently afford no information beyond mere ex- 
ternal appearance — but exhibits them archtteC' 
turaUy by means of plans, elevations, and occa- 
sionally both sections and interior perspective 
views. Thus a far more complete and correct 
knowledge may be obtained of each edifice, in its 
entire arrangement in all its parts and dimensions, 
than by pictorial views of them. 

As studies for the Architect, the subjects con- 
tained in these volumes strongly recommend them- 
selves, — more particularly so, as of the majority of 



them no plans and elevations are to be met with 
in any other publication, which materially en- 
hances the interest of this collection, and it pre- 
serves to us authentic and tolerably complete 
records of many buildings which no longer exist. 
Among these are Carlton House, illustrated 
with several plates, including sections, and a plan 
of the private apartments; the late English 
Opera House; Mr. Nash's Gallery, which 
has since been dismantled of its embellishments ; 
and The Royal Exchange. 

Among the subjects introduced in this New 
Edition will be found the following : — The Tra- 
vellers' Club House — London University 
— St. George's Hospital — Gateway, Green 
Park — ^PosT Ofpice — ^Fishmongers' Hall — St. 
Dunstan's, Fleet Street, &c. &c. 



62. 
Royal 8vo., 18 Engravings, doth boards, 10». 6J. 

ILLUSTRATIONS OF THE PUBLIC BUILDINGS OF LONDON, 

With descriptive Accounts of each Edifice. 

SUPPLEMENT : 

Containing the New Subjects and Descriptions by W. H. Leeds, incorporated in the second 
edition, and now sold separate for the accommodation of those possessing the first edition. 

Also a few copies in imperial 8vo. for large paper copies of the first edition, Price 15«. 



63. 
In demy 8vo., cloth boards, Price 9t. 

A TREATISE ON THE LAW OF DILAPIDATIONS AND 

NUISANCES. 

By DAVID GIBBONS, Esq., of the Middle Temple, Special Pleader. 

Dedicated to the Honourable Sir John Taylor Coleridge, Knt., one of Her Majesty's Justices of the 

Court of Queen's Bench. 



64. 
One large sheet, very accurately coloured, size within the line of work 25^ inches by 18^. Price 10«. 

GEOLOGICAL STRUCTURE OF ENGLAND, IRELAND, AND 

SCOTLAND. 

An Index Geological Map of the British Isles ; constructed from published documents, communications 

of eminent Geologists, and personal investigation. 

By JOHN PHILLIPS, F.R.S., G.S., Professor of Geology in King's College, London. 

Engraved by J. W. Lowry. 

Mounted in a case, Price 13#. ; on bhick roller, 16t.*, mahogany do., 18«. 



18 WORKS PUBLISHED BT JOHN WEALB^ 

65. 

J 

The foIloTving vexy valuable and interesting Work has been withheld from sale for sevcFal years: 
the publication price was fixed at £2, 2«., but, as a favourable purchase has been made, the price 
is now 16ff. in extra doth boards, and lettered. 

A SERIES OF ANCIENT BAPTISMAL FONTS, NORMAN, EARLY 
ENGLISH, DECORATED ENGLISH, AND PERPENDICULAR 
ENGLISH. 

Drawn by F. SIMPSON, Jun., and Engraved by R. ROBERTS. 

Large 8vo., contjuning 40 very beautifully engraved Plates, in the best style of the Art, and the Test ' 
written by an accomplished and talented Gentleman, whose attainments in Architecture and aa an Anti- 
quarian are well known and appreciated. 

A few copies on large paper, Price £1. 8t. ; and only six copies India prooft, with Etching!, at £2. 2t. 



66. 
One large 4to. The Plates engraved in the finest style of Art. Cloth boards, lettered, Price £1. lOt. 

THE MONUMENTAL REMAINS OF NOBLE AND EMINENT 

PERSONS, 

Comprising the Sepulchral Antiquities of Great Britain, engraved from Drawings by 

EDWARD BLORE, Architect, F.S.A. 
With Historical and Biographical Dlustrations. 

CONTBNTS. 

1. Eleanor, Queen of Edward the Fint. WeainUniter 17. John Q«mw. 8f. 5fltvio«r*« Ckurd^, Somikm^k.^ 

ilM«y.— 1990. 1408. 

8. Effigy of the tame. 18. King Henry the Fourth and hia QneeD. Cmmiertmrf 

3. Brian Fitcalan, Baron of Bedale. Bedale Church,^ CathedrtU,—Ul2, 
1301. 19. Effigy of Che lame. 

4. Aymer de Valenee, Eari of Pembroke. Weaitniruier 80. Thonuw Fitzalan, Earl of Arundd. AnttaM CJhcrcft. 
JMcy.— 1334. —1415. 

6. Sir Jamea Donglaa. Dowla$ Ckureh.^1931, 81. Ralph Neville, Earl of Wcataaorlaad. Stmm^r^ 

6. Gervaie Alard, Admiral of the Cinque Porta. Winehel' Church. — 1435. 

««a CAurvA.— No date. 88. Arehibald, 5th Bail of Douglaa. Dmtgin G^mrek.^ j 

7. Philippa, Queen of Edward the Third. WeutmihuUr 1438. 1 
Abbey. — 1360. 83. Richard Beauchamp, Earl of Warwi^ 



8. Effigy of the lame. Chapel, Warteiek.— 1439 

0. Thomaa Beauchamp, Earl of Warwick. Bemiehatnp 84. Effigyof the tame. 

Chapel. Warurick.^1970, 85. John Beaufort, Duke of SomerBOt. Wimharm MmUer. 

10. Edward, Prince of Walea. Canterbury Cathedral.-^ —1444. 

1370. 86. Humphrey, Duke of Olonceater. St, AWam*e JUcy.— 

11. Effigy of the same. 1446. 

13. King Edward the Third. Weatmimier Abbey.— 1377- 37. Sir John Spencer. Brington CAtirdh.— 1588. 

13. Effigy of the name. 88. Archbiahop* Warham and Peckham. Camierbmy 

14. Thomas Hatfield, Biahop of Durham. Durham Cathe- Cathedrat.—\i32. 
dral. — 1381. 99. Margaret Plantagenet, Goonteia at 

15. William of Wykham, Biahop of Winchester. Win- Church, Hampthire.—lSil. 
eheeter CaihedraL-~\ilH» 80. Sir Anthony Bxtmne. BaiU 

16. Effigy of the same. 



80. Sir Anthony Browne. BoMeilMqr.— IS48. 



67. 
In folio size, Price ;61. \$, in hoards. 

BRIDGEN'S INTERIOR DECORATIONS, DETAILS, AND VIEWS I 

OP SEFTON CHURCH, IN LANCASHIRE, 

Erected hy the Molineox family (the ancestors of the present Earl of Sefton), in the early part of the 
reign of Henry VIII. 

The Plates (34 in nnmber) display the beautiful Style of the Tudor Age in Details, Ornaments, : 
Sections, and ViewB. Etched in a masterly style of Art. | 

% 



ARCHITECTURAL LIBRARY, 59, HIGH HOLBORN. 



19 



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68. 
Royal 4 to., very neatly half-bound in morocco, gilt. Price £2. I2s. 6d. 

DRAWINGS OF THE FINEST EXISTING SPECIMENS OF 
ANCIENT HALF-TIMBERED HOUSES OF ENGLAND, 

And of their Details ; with an Essay, showing the Classification of the Style, and the Age to which it 
belongs. 

By M. HABERSHON, Architect. 

%* The work contains upwards of Twenty Views, taken from the finest remaining Specimens of this 
interesting branch of the Ancient Architecture of England, comprising Manor Houses, Town Resi- 
dences, and Cottages, some of which are particularly striking and picturesque ; and, in order to give a 
more complete illustration of it, such Views are accompanied by Drawings, to a large scale, of Chim- 
neys, Tracery, Porches, Doors, Windows, and other Details. To which is added, an Essay, giving a 
General Historical View of English Architecture. 



69. 
With Plates, imperial 8vo., cloth boards, £1. 1». 

CLARKE'S ELIZABETHAN ARCHITECTURE. 



Wimbledon Honse, Suxrey, built by Sir Thomas 

1588. 
Easton House, Esiicx, Sir Henry Majmard. 
AKton Hall, Warwickshire, Sir Thomas Holt. 
Grafton Hall, Cheshire, Sir Peter Warburton. 
Stanfield Hall, Norfolk, family of Flowerdews. 
Seckford Hall, Thomas Seckford. 
Bramshill House, Hampshire. 
Fenn Place, Kent, Lord Zouch. 
Queen's Head, Islinpton, Sir Walter Raldgh. 
ChasletOD, Ozfordahure, Walter Jones. 



CONTENTS. 

Cecil, Brereton Hall, Clieshire, Sir Walter Brereton. 
Holland House, Middlesex, Sir Walter Cope. 
Haughley House, Suffolk. 
Streete Place, Sussex, Dobell. 

Montacute House, SomersetsluTe, 8ir Edward FliiUpa. 
Westwood House, Worcestershire. 
Wakehurst Place, Sussex, Sir Edward Culpeper. 
Carter's Comer, Sussex. 
Eastbuiy House, Essex, Lord Monteagle. 
East Mascall, Sussex, Newton. 
Old House, near Worcester, &c. 



70. 

Sixty Plates, Title-Page printed in colours and gold, el^^^^^^y half-bound in morocco, and lettered, 

Price £1. 16«. 

SPECIMENS OF THE ARCHITECTURE OF THE REIGNS OF 
QUEEN ELIZABETH AND KING JAMES L, 

From Drawings by Charles Jambs Richardson, Gborob Moorb, and other Architects, with 
Observations and Descriptions of the Plates. 

Eighteen Plates iUustrate the Old Manor House, the Gardens, Terraces, &c. at Claverton, the Seat of 
George Vivian, Esq. — six the Duke of Kingston's Picturesque House at Bradford — and eight the 
princely Mansion of Lord Holland at Kensington. 

The volume contains examples of Ceilings, Porches, Balustrades, Screens, Staircases, Monuments, 
Pulpits, &c. ; and a rich collection of Facsimiles of Old English Drawings, chiefly of John Thorpe, 
the most eminent Artist in Qaeen Elizabeth's time. 



71. 

In 8vo., extra cloth boards, and lettered, Price 7«. — 25 copies are printed on India paper, Price lOt. M. 

Second Edition, corrected. 

HAKEWELL'S ATTEMPT TO DETERMINE THE EXACT 
CHARACTER OF ELIZABETHAN ARCHITECTURE, 

Illustrated by Parallels of Dorton House, Hatfield, Longleate, and Wollaton, in England ; the Pallazzo 
della Cancellaria, at Rome. 

The Plates (8 in number) consist of compartments of the Pallazzo della Cancellaria, at Rome, by 
Bramante, 1495; and Longleate, by John of Padua, 1547. Compartment of the South Front of 
Hatfield, 1611, with comptftroent of WoUaton Hall, 1580; Dorton House, Bucks — a Plan, Screen in 



-% 



% — 

20 WORKS PUBLISHED BY JOHN WEALB^ 



the HaU ; Longitudinal Section of the Staircase ; Transrene Section of the Staircase ; ChimiieT-piece 
in Queen Elizabeth's room ; Ceiling in the same room ; a front view of the Queen occupies the centre 
compartment ; the corresponding compartments are filled with the Portraits of her principBl Blinisters 
in profile. 

72. 

8vo.| cloth boards, and lettered, Price S$. ' 

MOLLER'S GERMAN GOTHIC ARCHITECTURE, 

Translated With Notes and niustrations by W. H. LEEDS. 



73. 
In 8vo., with Notes and Illustrations by W. H. LEEDS. Price £4. 4#. 

German Satbic ^SLxtbittctavt. 
MEMORIALS OF GERMAN A-RCHITECTURE; 

Or, the ARCHITECTURAL ANTIQUITIES OF GERMANY. 

By GEORGE MOLLER, of Darmstadt, Architect to the Grand Duke of Heaae. 

2 vols., large folio, with 130 Plates, a Description of each Edifice, and an Essay on the Origin and Pro- 
gress of Gothic Architecture, with reference to its Origin and Progress in England ; in the German 
Language, accompanied by an English Translation. 

' The Tnuitition, or Early German, haa not yet« ao far more will probably appear in a abort time. Dr. MoDer't 
aa I knoWj receired much matinct attention. Dr. MoUer, work (Denkmaehler der Deutachen Banknnat) alraadT coo- 
however, in the course of hia valuable Denkmaehler, baa tains excellent specimens of every style of German bniU- 



recentlv given na excellent representations of the Cathedral inga, and offera additional intereat and bcanty in _„ 

at LimbuTj^, on the Lahn, which ia a very admirable sped- number.' — Whewell's Notes on German Chuvdies, pp. 

men of thia kind ; and has noticed the intermediate and 28, 20. 

transition place which this edifice seems to occupy in the * The Church of St. Catharine, at Oppenbcim, near 

developement of the German atyle.' — Whewell's Notes on Worms, also in part a ruin, ia another fine example of this 

German Churches, p. 25. style, and has been worthily illustimted in the mafptificent 

' There exist, however, several valuable pnblicationa, with work of Dr. MoUer.' — Whewell'a Notea on Gcroua 

good pJatea, on the sul^ect of German Architecture, and Churches, p. 113. 

Sereral copies of Seventy-two Plates, making Vol. I., have been sold in this country : some copies of 
the 2nd Vol. to make up these sets can be had for £2, 12«. 6J. 



74. 
Royal 4to., with Plates. Price £1. U. 

PROLUSIONES ARCHITECTONICiE ; 

Or, ESSAYS on Subjects connected with GRECIAN and ROMAN ARCHITECTURE. Dlostrated br 
Forty Engravings by eminent Artists. Dedicated, by permission, to Eabl Grst, ILG. 

By WILLIAM WILKINS, A.M., R.A., P.R.S., 
Formerly a Senior Fellow of Caius College, in the University of Cambridge ; Professor of Ardiitectare 

in the Royal Academy of Arts. 



75. 
2 vols 4to., upwards of 70 Plates and Wood-cuts, Price £2. 2f. 

LETTERS OF AN ARCHITECT FROM FRANCE, ITALY, 

AND GREECE; 

Or, CRITICAL REMARKS on CONTINENTAL ARCHITECTURE, ANCIENT and MODERN, and 
on the CLASSIC ARCHITECTURE of GREECE. Written in a Series of Letten. 

By JOSEPH WOODS, F.A.S., F.L.S., F.G.S., &c 
— # 



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ARCHITECTURAL LIBRARY^ 59, HIGH HOLBORN. 21 | 

76. 
8vo.» with Plates, Price 7#. 

VENTILATION, WARMING, AND TRANSMISSION OP SOUND. 

REPORT OF THE COMMITTSB OF THE HOUSE OF COMMONS ON VENTU^TION, WARMING, 

AND TRANSMISSION OF SOUND, 

Abbreviated, with Notes. By W. S. INMAN, Architect, F.I.B.A. 



77. 

In 8vo., illustrated with a very fine Frontispiece of St. Paul's Cathedral, by Gladwin. Extra 

cloth boards. Price 10«. 6 J. 

THE PROFESSIONAL PRACTICE OF ARCHITECTS AND THAT 

OF MEASURING SURVEYORS, 

And Reference to BUILDERS, &c., &c., from the time of the celebrated Earl of Burlington. 

By JAMES NOBLE, Architect, F.I.B.A. 



78. 
78 very fine Plates, royal foHo, neat in cloth boards and lettered, Price £3. 3#. 

THE UNEDITED ANTIQUITIES OF ATTICA. 

By the Society of DilettantL Comprising the Architectural Remains of Eleusis, Rhamnus, Sunium, 

and Thoricus. 



79. 
8vo., with Plates, Price 7«. 

COTTAGES AND HOUSES FOR THE PEASANTRY AND 

EMIGRANTS. 

ELBMBNTART AND PRACTICAL INSTRUCTIONS ON THB ART OF BUILDING COTTAGES AND HOUSES 

FOR THE HUMBLER CLASSES. 

An Easy Method of Constmcting Earthen Walls, adapted to the Erection of DweDing-hoiises, Agri- 
cultural and other Buildings, surpassing those built of Timber in comfort and stability, and equalling 
those built of Brick, and at a considmble saving. To which are added, Practical Treatises on the 
Manufacture of Bricks and Lime ; on the Arts of Digging Wells and Draining ; Rearing and Managing 
a Vegetable Garden ; Management of Stock, &c. For the use of Emigrants ; for the better Lodging <2 
the Peasantry of Great Britain and Ireland ; and the Improvement of those Districts to which the 
benevolence of Landed Proprietors is now directed. 

By WILLIAM WILDS, Surveyor. 

The work contains : — 

Chap. I. The Art of Conttruetinff Houms and Cottages IV. On the Propertiei, Usee, and Manufuture of lime, 

with Earthen Walla nuule easy, being^ intellinble to all V. On Well-dining, Draining, WeU-ainking, ftc. ; on 

claaaes, and to the moat ignorant m building, with Fuel, on Oardening ; what quantity of Land will keqp a 

Wood-cttta of tools, plans, and sections, &e. Family in culinary VM;etables ; Fork, Ens, Milk, and 

II. On Bricks, how they are to be advantageoualy applied Bread Com ; on the Keeping of Gowa, Hogs, Ponlt^, 
in conjunction with rammed earth ; rules for selecting Beea, and Art of making of Candles, So^, Storing Fruit, 
tiie best earth, &c. Roots, &c. 

III. On the Manu&cture and Choice of Bricks. 



80. 
In 4to. Plates, very neatly coloured, cloth boards and lettered, Price 16«. 

A SERIES OF DESIGNS FOR VILLAS AND COUNTRY HOUSES, 

Adapted with Economy to the Comforts and to the Elegances of Modem life, with Plans and 

Explanations to each. 

By C. A. BUSBY, Ar^hi^^ 

# 



m 



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22 WORKS PUBLISHED BY JOHN WEALE^ 

81. 
Second Editioiii 4to., Price £1. It. 

DESIGNS FOR VILLAS AND OTHER RURAL BUILDINGS. 

By the late EDMUND AIKIN, Architect. 

Engraved on 31 Plates, with Plans and Elevations, elegantly coloured, and an Introductory Essay, 
containing Remarks on the prevailing Defects of Modem Architecture, and on the Investigation of the 
Style best adapted for the Dwellings of the Present Times. Dedicated to the late Thomas Hope, Esq. 

' Modem Architects profess to imitate anticme examples, which is superior to the details that poide them? This is 

and do so in colmnns, entablatures, and detaus, but never a subiect which it may be useful and mterestiDg to puxvoe.' 

in the general effect. Is it that they imitate blindly, and — Vide Introduction, 
without penetrating into those pxinciples and that system 



82. 

16 Plates, large 4to., Price I6s. 

DESIGNS FOR RURAL CHURCHES. 

By GEORGE E. HAMILTON, Architect. 



83. 
Second Edition, in 8vo., iUustrated with numerous large folding Plates, Price 12#. 6J. 

A POPULAR TREATISE ON THE WARMING AND VENTI- 
LATION OF BUILDINGS, 

Showing the advantages of the Improved System of Heated Water Circulation, &c. &c. &c. 

By CHARLES JAMES RICHARDSON, Architect 



84. 
The Sixth Edition, Price 18«. bound. 

THE PRACTICAL HOUSE CARPENTER, OR YOUTH'S 

INSTRUCTOR ; 

Containing a great variety of useful Designs in Carpentry and Architecture ; as Centering for Groins, 
Niches, &c. ; Examples for Roofs, Skylights, &c. ; Designs for Chimney-pieces, Shop l^nts. Door 
Cases; Section of a Dining-Room and Library; variety of Staircases, with many other important 
Articles and useful Embellishments. The whole illustrated and made perfectly easy by 148 4to. 
Copper-plates, with Explanations to each. 

By WILLIAM PAIN. 



85. 

In small 8vo., for a Pockel-Book. A New Edition, with the Government Tables of Annuities. 

Price 79, boards. 

TABLES FOR THE PURCHASING OF ESTATES, 

Freehold, Copyhold, or Leasehold, Annuities, &c, and for the Renevring of Leases held under Cathedral 
Churches, Colleges, or other Corporate Bodies, for Terms of Years certain, and for Lives ; also, for 
valuing Reversionary Estates, Deferred Annuities, Next Presentations, &c. Together with several 
useful and interesting Tables connected with the subject. Also, the Five Tables of Compound Interest. 

By W. INWOOD, Architect and Surveyor. 



86. 
12mo., Price 3». 6<f. 

A MANUAL OF THE LAW OF FIXTURES- 

By DAVID GIBBONS, Esq., of the Middle Temple, Special Pleader. 
%* A work purposely written for the use of Builden, House Agents, and House and Land Proprieton. 

9 « 



^ 

ARCHITECTUBAL LIBRARY^ 59^ HIGH HOLBORN. 23 

87. 
Price 2«. 6d,, pocket size, cloth boards. 

THE BUILDING ACT (at Large), side References. 

With Extracts from the Sweeps' Acts; and with Explanatory Notes and Cases. 

By A. AIN6ER, Architect. 



88. 
8vo., Price 16*. 

COMPLETE ASSISTANT for the Landed Proprietor, Estate and House 

Agent, Land Steward, Proctor, Architect, &c. 






89. 
8vo. volume, with a folding Plate, Price 5«. 

ON THE SAFETY LAMP, 

For Preventing Explosions in Mines, Houses Lighted hy Gas, Spirit Warehouses, or Magazines in 

Ships, &c. ; with Researches on Flame. 

By SIR HUMPHREY DAVY, Bart. 



90. 
New Edition, 8vo., Price 16«. With 35 Copper-plate Engravings. 

A TREATISE ON ISOMETRICAL DRAWING, 

As applicable to Geological and Mining Plans, Picturesque Delineations of Ornamental Grounds, Per- 
spective Views and Working Plans of Buildings and Machinery, and to General Purposes of Civil 
Engineering; with Deteuls of improved Methods of preserving Plans and Records of Subterranean 
Operations in Mining Districts. 

By T. SOPWITH, M.I.C.E. 



91. 
Second Edition, with Examples, Price 3». 6J. 

A SET OF PROJECTING AND PARALLEL RULERS, 

For constructing Working Plans and Drawings in Isometrical and other Modes of Projection. 

Invented by T. SOPWITH. 



92. 
Price 10». 6d. 

GEOLOGICAL SECTIONS 

Of Holyfield, Hudgill Cross Vein, and Silver Band Lead Mines, in Alston Moor and Teesdale, showing 
the various Strata and Subterranean Operations. Engraved on three coloured Plates, vrith De- 
scriptions, &c. 



93. 
12mo., Price 4«. 6 J. 

AN ACCOUNT OF THE MINING DISTRICTS 

Of Alston Moor, Weardale, and Teesdale, in Cumberland and Bui^»xxi ; Descriptive Sketches of the 
Scenery, Antiquities, Geology, and Mining Operations in the lloDer Dales of the Bivers Tyne, Wear, 
and Tees. ^^^ \ 






m- 



24 



WORKS PUBLISHED BY JOHN WEALE^ 



94. 
In 4to., with 5 Plates, in boards, Price 10«. M. 

OBSERVATIONS ON THE CONSTRUCTION AND FITTING UP 
OF MEETING HOUSES, &c. FOR PUBLIC WORSHIP; 

Illustrated by Plans, Sections, and Descriptions, including one erected in the City of York ; 

in particular, the METHOD of WARMING and VENTILATING. 



FURNITURE AND INTERIOR DECORATIONS. 



95. 

Royal 4to., Price £1. U. 
CHIPPENDALE'S 133 DESIGNS OF 
INTERIOR DECORATIONS IN THE OLD 
FRENCH STYLES, for Carvers, Cabinet- 
Makers, Ornamental Painters, Brass-Workers, 
Modellers, Chasers, Silversmiths, General De- 
signers, and Architects. Fifty Plates 4to., con- 
sisting of Hall, Glass, and Picture-Frames, 
Chimney-Pieces, Stands for China, &c.. Clock 
and Watch Cases, Girandoles, Brackets, Grates, 
Lanterns, Ornamental Furniture, and Ceilings. 

96. 

15 Plates, 4to., Price 10«. M, 
SPECIMENS OF THE CELEBRATED 
ORNAMENTS and INTERIOR DECORA- 
TIONS of the AGE of LOUIS XIV., selected 
firom the magnificent work of Meissonnier. 

97. 
11 Phites, 4to., Price Is, 

CHIPPENDALE'S DESIGNS for 
Sconces, Chimney and Looking-Glass Frames, 
in the old French style: adapted for Carvers 
and Gilders, Cabinet-Makers, Modellers, &c. 

98. 

12mo., Price 4«. 6J. 

DESIGNS FOR VASES, on 17 Plates. 

99. 
10 Plates, 8vo., Price 4«. 

DESIGNS FOR CHIMNEY-PIECES 
AND CHIMNEY GLASSES, the one above 
the other, in the times of Inigo Jones and Sir 
John Vanbuigh. 

100. 
5 Plates, oblong, Price 1«. 6<f. 

A BOOK OF ORNAMENTS, suitable 
for Beginners. By THOMAS PETHER, 
Carver. 

101. 

In large folio, 126 Plates, boards, Price M. 4«. 

ETCHINGS, representing the BEST 
EXAMPLES of ANCIENT ORNAMENTAL 
ARCHITECTURE, drawn from the Originals 
in Rome. FRAGMENTS of GRECLA.N OR- 
NAMENT. By C. H. TATHAM, Architect, 



102. 

On 33 folio Plates, engraved in imitation of 
Chalk Drawings, Price 15a. 

ORNAMENTS DISPLAYED, on a fall 
size for working, proper for all CarverBy PaiBien, 
&c., containing a variety of Accurate F-rMiwpU* 
of Foliage and Friezes. 

103. 

With 30 Plates, coloured in a superior manDer 
and hot-pressed, bound in ckith, and gold 
lettered, with a letter-press descriptive Kit of 
the contents. Price £1. 7t. 

DESIGNS OF VALANCES AND DRA- 
PERIES, consisting of New Designs liar Fkahion- 
able Upholstery Work. By T. KING. 

This work contains a variety of Yalanoes and 
Draperies of the richest description, adapted 
for Dining and Drawing-rooms, with many 
novel Designs for Four-post and French Beds. 

As a limited number of this work is prepared, 
orders are requested as eariy aa possible. 

104. < 

46 Coloured Plates, oblong, Prioe £\, 

ORIGINAL DESIGNS FOR CABINET ' 

FURNITURE. By T. KING. 

105. 

32 Coloured Plates, oblong, Prioe £V. 

ORIGINAL DESIGNS FOR CHAIRS J 
and SOFAS, vnth MUSIC STOOLS, FOOT , 
STOOLS, OTTOMAN SEATS, &c Ac By 
T. KING. , 

106. 

Part I., large quarto, 16 Plates, Prioe 12t. 

THE UPHOLSTERER'S SKETCH- ■ 
BOOK OF ORIGINAL DESIGNS FOR 
FASHIONABLE DRAPERIES. By T. KING. 

107. 
Price 12f. 

THIRTY-SIX NEW. ORIGINAL, AND 
PRACTICAL DESIGNS for CHAIRS, adapted 
for the DRAWING and DINING-ROOM. 
PARLOUR and HALL. By W. TOMS, junior, 
Carver. 

« 



r 



ARCHITECTURAL LIBRARY^ 59^ HIGH HOLBORN. 



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108. 

Parts 1, 2, 3, 4, complete, lOt. 6<f. each, (the 
whole £2. 2s.,) containuig 84 Plates. 

AN ENTIRE NEW SERIES OF 
CABINET AND UPHOLSTERY DESIGNS, 
intended to embrace eyery variety of elegant 
and useful Furniture, suited to the Palace or 
Cottage, including the various styles of Greek, 
Gothic, Louis the 14tb, &c. By GEORGE 
SMITH. 

109. 

Price £1., 4to. post, common paper, 15»., contain- 
ing 37 Phites, and 44 pages of letter-press. 

UPHOLSTERERS' ACCELERATOR, 

Being Rules for Cutting and Forming Draperies, 
Valances, &c,, accompanied by appropriate Re- 
marks, and containing a full description of a New 
System, which will greatly facilitate and improve 
the execution. By T. KING. 

110. 

On 80 Plates, conveniently small for the pocket, 

Price £1. 3«. 

DECORATIONS FOR WINDOWS 
AND BEDS. 

I Consisting of 100 Fashionable Designs for Uphol- 
I stery Work, with the Varieties of the present Style, 
divided into parts. By T. KING. 

111. 

; Price 15*. coloured, containing 21 Plates, 4to. 
j demy, half-bound. 

MODERN DESIGNS FOR DRAPERY 
AND VALANCES. 

Displayed in Beds and Windows. 
By T. KING. 

112. 

Just published, 3 Parts, Price £1. 10*. 

WORKING ORNAMENTS AND 
FORMS, 

Full size, for the ase of the Cabinet Manufacturer, 
Chair and Sofa Maker, Carver, and Turner. 

By T. KING. 
113. 



2 vols., large 4to., 60 Plates, Price £2. 5«. 
CABINET-MAKERS' SKETCH 

BOOK. By T.KING. 



114. 

Price £L 
SUPPLEMENTARY PLATES 

To the work entitled "The Modem Style of 
Cabinet Work Exemplified in New Designs.^' 

By T. KING. 

The Supplementary Plates consist of 68 New 
Designs, on 28 Plates. 

115. 

Price £2., mediom 4to., half-boimd; common 
edition, £1. 12«. in boards. 

THE MODERN STYLE OF CABINET 
WORK EXEMPLIFIED IN NEW 
DESIGNS, 

On 72 Plates, contsining 227 Designs for Cabinet 
Work. By T.KING. 

116. 

Price £1., 42 Plates, on royal 4to., many of which 
are neatly coloured. 

DESIGNS FOR CARVING AND 
GILDING, 

With Original Patterns for Toflette Glasses. 
By T. KING. 

117. 
Price 5»., 8vo. 

R. MAINWARING'S CHAIR- 
MAKERS' GUIDE. 

200 Genteel Designs (1766). 

118. 

Large 8vo., Price 7«. 
HOUSEHOLD FURNITURE. 

In the taste of a century ago, containing upwards 
of 350 Designs on 120 Plates. 

119. 
Price 15«., 18 Plates, on folio demy. 

SHOP FRONTS AND EXTERIOR 

DOORS, 

Displaying the most approved of London execu- 
tion, and selected aa bdng those of the best taste 
and greatest variety ; drawn to a scale by accurate 
measurement accompanied by the proper Sections 
and Plana, with several l^ew Pracdod Dengns : 
for the uae ^f tb^ Architect, Builder, and Joiner. 
By T. KIJ^^' 



26 



WORKS PUBLISHED BY JOHN WBALE^ 



120. 
Omamentil* 

GRECIAN ORNAMENTS. 

A SERIES of EXAMPLES, in 21 Plates, of GRECIAN ORNAMENT, in royal folio, tot M 
engraved from Dravdngs made by the most celebrated Architects. I^ce lbs, 

CONTENTS OF THE WORK* 

Restored Elevmtion to the Entnnce of tbm Sohtatarn 

Chambers at Mjceam, oonunoolj called tlie TteaMr J 

Atreus.' 
Marble Stele, in the poMesaion of Mr. Gropina, at Atka^ 
Terracotta Antefiza, at Athena, and MacUc Frapva 

from I>elphi. 
ISIaater Capitals from Stratonice and HalienmaaaBt. 
Fragments from Halicamassus, Teoa, and Teaiple i 

Apollo, at Branchydte, near MQetoa. 
Entasis of the Columns of the Portico of the Prap^Ict- 

of the North Wing of the Propylsea. 

of the Temple of llieseus. 

of the Temple of Minerra, or Parthenon. 

of the Chonigic Monument of LjsicEates. 

of the Columns of the NorUi Portico of the T-,- 

Temple, termed the Erecbtheum. 

of the Columns of the East Portieo of that Tes;« 

of Ae Temple of Jupiter PanheUeaiua, at .Cf.e. 

of the Columna of the Prooaos of the »>: 



Details of the Ceiling of the Prapylaa, at Eleusia. 

Order of the Antae ofthe Inner Vestibules, at Elensis. 

Capital of the Antse at lar^, at Eleusis. 

Fragments found at Eleusu. 

Tiles and other Details of the Temple of Diana Propyliea, 
at Eleusis. 

Capitals and Profile of the Temple of Nemesis, at Rham> 
nus. 

Ornamental Moulding, Jamba, Mouldings of Interior Cor- 
nice, the Painted Bf ouldings of the F^eis of the Lacu- 
naaia, &c. &c. of the Temole of Nemesis, at Rhamnus. 

Details of the Roof, Tiling, oec. of the Temple of Nemesis, 
at Rhamnus. 

The Chairs and Sepulchral Bas-reUe& found in the Cella of 
the Temple of Tnemis, at Rhamnus. 

Athenian Sepulchral Marbles, Capitals, and Triglyphs, at 
Delos. 

Entablature of the Order of the Pejistyle and Roof, Orna- 
ments, &c. of the Temple of Apollo Epicurus, at Bassee. 

Details of Sculptured and Painted Shafts of Columns of the 
Subterraneous Chamber, at Mycenae. 



Temple. 



This work is very desirable for Sculptors, Modellers, Masons, (in designing for Monuments, Tor' 
Tablets, &c.) Builders, and Architects. Those who possess the Dilettanti work of the Vnei^J 
Antiquities of Attica, and the Supplementary volume of Antiquities of Greeoe, Sicily, Jcc, will doc zh^ 
this work, as the subjects are selected from them. 



VALUABLE ENGRAVINGS ON ARCHITECTURE, CIVIL AND 

MECHANICAL ENGINEERING. 



121. 

LONDON BRIDGE : engraved on Steel, 
in the best style, by J. W. Low&y, under the 
direction of B. Albano, Esq., C.E., from his 
Drawing presented to the Institution of Civil 
Engineers, and made from the Original Draw- 
ings and Admeasurement, vnth permission of 
ISir John Rennie, F.R.S., the Engineer. 1st. 
Part. Plan and Elevation on a large scale, 25 
feet to 1 inch. lbs. On India Paper, £1. Iff. 

122. 

STAINES BRIDGE : a fine Engraving 
by J. H. Lb Keux, under the direction of 
B. Albano, Esq., C.E., from his Drawing pre- 
sented to the Institution of Civil Engineers, 
and made from the Original Drawings and 
Admeasurement, with permission of George 
Rennie, Esq., F.R.S., the Engineer. 1st. Part. 
Plan and Elevation on a scale of 10 feet to 
1 inch. lOff. On India Paper, lbs. 

123. 

PARIS — Bridge of JENA, 2 fine Prints. 
Plan, Elevation, Section, and Details. Draw- 
ings made by L. Golembrowski, C.E. (Polish 
Engineer residing in Paris), from admeasure- 
ment, by permission ofthe French Government. 
lOff. 



124. 

GLADWIN'S Fbe Engraving of ^ 
Patent Self-Acting Slide Lathe, manufacrj* 
by Messrs. J. WHrrwoRTH and Co., M^ 
Chester. 5ff. India paper, 7». 6d. 

125. 

GLADWIN'S Fine Engraving of a Drl 
ing and Boring Machine, by Mesaia. Wu. 
WORTH and Co., Manchester. 7s. 

126. 

GLADWIN'S Elevation of Stbphkn»» 
Patent Locomotive Engine, printed on Vi 
paper for colouring. Columbier aize. 3«. 6« 

127. 

GLADWIN'S Splendid EngraTing 
Stephenson's Patent LocomotiTe Eogiue. 
Large folio, Price 7s. 
%* This is a master-piece of Mechanical ' 
graving, and may be considered unique it 
execution. 

128. 

Lithographed Folio Print of the Vcr 

brated Train Carriage for Railways, to disti 

Friction and Concussion. Mr. B. .Vp> 
Patentee. 2s. 



ARCHITECTURAL LIBRARY, 59, HIGH HOLBORN. 



27 



129. 
Price £1. 8«. 

LERRISSEAU'S Fourteen Plates of 
Engravings, on a large Atlas folio size, of the 
following, being a set. 

Arch of PoU in Istria. 

Arch of Traian. 

Temple of PoU in Istria. 

Temple of Venus. 

Amphitheatre of Capua. 

Inside of the Temple of Concord. 

Ancient Sepulchre situated in Naples. 

Arch of Septimus Severus and of Caracalla. 

Amphitheatre of BeneTentum. 



Temple of Serapb. 

Tomb of Virgil. 

Temple of Jupiter Statof . 

Temple of Antoninus and Faastina. 

Gate of Ciuna. 

130. 

Gilt frames and glazed, very neat, llff. the pair. 

PORTRAITS FRAMED AND GLAZED 
FOR AN OFFICE. 

A Pair of Portraits of Geo. Stephenson, Esq., 
of Newcastle upon Tyne, and Robert Steven- 
son, Esq., of Edinburgh, Civil Engineers. 



131. 
Handsomely engrayed on Steel, (size 16 inches by 10^ inches,) Price 2«. 6d. plain, 3«. coloured. 

A CHART OF THE HARBOUR AND PORT OF 

LONDON, 

iliibiting the River Thames and the adjacent Docks from London Bridge to Bugsby's Hole, and 

eluding the Greenwich Railway, the Commercial Railway, and the commencement of the Croydon 

ilway. 

In this Chart the Low-water Mark, Soundings, Shoals, and other important features, are inserted 

tm the most recent surveys ; and, from the care which has been exercised in indicating correctly thti 

nous Mfliarfs, Dock-yards, Warehouses, and Factories, on each side of the River, it will be found of 

i&i utility to all persons engaged in nautical or commercial pursuits. 



SIR CHRISTOPHER WREN'S 
ARCHITECTURE. 

SS. Plan of hia First Design of St. Paul's, U. 

33. Elevation and Section of Bow Church, 1«. 6tf. 

34. Interior of St. Stephen's, Walbrook, U. 

35. Section of St. James's Church, PiccadiUy, 1«. 

36. Roof of the Theatre at Oxford, l«. 

37. Plan for the Rebuilding of the City of London, U. 

38. Elevation, Plan, and Section of the College of Phy- 
ans, London, 1«. 6d. 

39. Elevation of the Tower and 8pii« of St. Dunstan's 
::be East, London — ^Elevation and Section of Chichester 
xe, l«. 6d. 



140. 

WESTMINSTER HALL. 
Section from admeasurement by Mr. George Allan, 
(Clerk of the Works to Sir Robert Smirke, Architect to the 
late Renovation). Very neady engraved by Mr. Hawks- 
WOBTH. Folio sixe, 2t. (id. 

141. 

SECTION OF ST. PAUl's CATHEDRAL. 

ThK OaiOINAL SrLBTTDID ElfOBAYINO by GWYN, of 

the Section of St. Paul's CATHanaAi., decorated 
agreeably to the original intention of Sir Christopher 
Wren; a very fine Urge Print, showing distinctly the 
construction of that magnificent Edifice. Price lOi. 

This is a magnificent Plate, the only one of its kind, 
showing constructively the genius of Sir Christopher Wren. 



The follonnng Prints, 8vo. size, are 6J. each ; 4to. size, on India paper, 1«. each. 



47. 

48. 

i9. 

30. 
51. 



42. Mr. Greenough's Villa. 2. D. Burton. 

43. Catholic Chapel, s. Newman. 

44. York Stairs' Water Gate. 1. I.Jones. 

45. Somerset House, (Elevations, Interiors, aodViewt). 
Chambers. 

46. Society of Arts. I. Adam. 
CKillcge of Physicians. 2. Wren. 
Newgate. 1 . Dance. 
Church of St. Peter le Poor. 1. Gibson. 
East India House. 1 . Jupp. 
Ashbumham House. 2. 1. Jones. 

52. Church of St. George. 3. Hawkamoor. 

53. Church of All Souls. 1. Nash. 

54. Westminster Hall. 9. Nash. 

55. Banqueting House. 1. I. Jones. 
50. Mansion House. 1. Dance, &c. 

57. County Rre Office. 1. Abraham. 

58. University Club House. 1. Wilkins and Gandy. 

59. Tower of Bow Church. 1. Wren. 

60. Westminster Abbey Church. 0. Wren. 

61. Hall, Christ's Hospital. I. Shaw. 

62. Carlton Palace, fl. Sir R. Tavlor. 

G3. College of Physicians and Umon Club House. S. 
R. Smirke. 



164. Terraces in the Regent's Park. 9. Nash and D. 
Burton. 
Ids. Council OiBce, ftc. 1. Soane. 
106. Bank of England. 3. Soane. 

167. Law Courts, Westminster. 3. Soane. 

168. House of Lords, &c. S. Soane. 

169. Colosseum, Regent's Park. 1. D. Burton. 

170. Hanover Chapel. 1. CockereU. 

171. Temple Bar. 1. Wren. 

172. House of Mr. Nash, &c. 2. Nash. 
17s. Belgrave and Eaton Squares. 2. Nash. 

174. Mr. Kemp's Villa. 2. Kendall. 

175. London, Southwark, and Waterloo Bridges. 
Bennie. 

176. Bridge of Blackfnars. 1. Mylne. 

177. Bridge of Westminster. 2. Labelye. 

178. King's Entrance, House of Lords, Section and In- 
terior Views. 8. Soane. 

170' Plan and Interiors of St. Stephen's, Walbrook. 2. 
Wren. 

180. Plan and Interiors of Temple Church. 3. Wren. 

181. Plans, Elevation, and Section of Custom House, 
London. 2. Laing. 

189. Plan and Elevation of Uxbridge House. Vardy. 



6. 



# 



183. PUns, Elevations, Vmwb, and Seckuma of St. Paul'a 
Cathedral. 8. Wxen. 

184. Elerations and Seetioni of St. Maxtin't Choxcli. 8. 
Gibba. 

185. Flan, Section, and Ele¥ati<m of the Qiieen*t Theatre. 
S. NMh and Repton. 

186. Flan and Elevation of the Diorama. Piigin and 
Morgan. 

187. Flan, Elevation, and Interior View of Haymarket 
Theatre. Nuh. 

188. Flan, Side Elevation, and Interior of Weetminster 
Abbey. 2. 

189. Flan, Elevation, Section, and Interior of St. Mary 
Woolnoth. 2. Hawknnoor. 

100. Flan, Elevation, and Section of St. F1ulip*t, Regent 
Street. 9. Rmton. 

101. Flan ana Elevation of Bethlem Hoepital. Lewis. 
iga. Flan and Elevations of Burlington Hoose. Lord 

Burlington and Colin Campbell. 

103. Elevation and Secti<ms of St. Bride's Choreh. S. 
IK^ren. 

104. Interiors of Sir John Scene's House. S. Soane. 

105. FLan, Elevation, and Section of St. Paul's, Covent 
Garden. Iniso Jones. 

106. Elevation of the Royal Exchange. 9. Jeiman. 

107. Flan and Elevation of the Russell Institution. 

106. Interiorofthe Mansion of Thos. Hope, Esq. a. Hope. 

100. Flan, Elevation, and View of the library of the 
London Institution. 9. Brooks. 

900. Flan, and Transverse and Longitudinal Sections of 
King Henry Tth's Chapel. 9. Begun 1509. 



901. Flan, Elevations, Interiora, and Seetioia 
Garden llieatre. 6. Sir Robert Smirke. 

909. Flan and Elevation of Sir John Naah'an 
90S. Flan and Transverse Section of St. Jaataca'a^ 

dilly. Wren. 

904. Interior of Freemasons' Hall. Sandbr. 

905. Flan, Elevation, and Sections of St. JLoke'a 
Chelsea. 9. Savage. 

906. Elevationa, Seetiona, and Plan of St. 
Church. 8. Inwood. 

907. FUn and Elevation of All Sainta GbmcAi, 
HoUis. 

908. Elevation and Section of St. Dnnsten'a m Oe 
Wren. 

900. Elevation and Section of Bow ChmA. ITia 

910. Flan and Elevation of St. 
Hardwidw. 

911. Flan, Sections, and Interior of tlM 
Chiqpel, Moorflelds. 8. Newman. 

919. Flan, and Garden F^ont of the British 
(Old). Fouget. 
9IS. Flan and Elevation of the Horse Gimvda. 

914. Flan and Elevation of the Villa of Ji 
Esq. Burton. 

915. View of the East side of Belgravna S<iaaK. 

916. Flan, View, Sections, and Intetiora of 
Tlaeatre. 6. B. Wyatt. 

917. View of the Interior of the English Opcfa 
Beasley. 

918. View of the Interior of the AmphitficBfif , 
minster Bridge. 



910. View of the Five Elliptical Arch Bridge across the 
Tweed at Kebo. Constructed by the late John Rennie, 
Esq., Civil Engineer. Laxf^ print, 5«. 

990. View of the Centering of Blackfriars' Bridge, by R. 
Mjrlne. Engraved by the celebrated FiranM. Large 
prmt, 4«. 6d, 

991. View of the Progress of the First Arch of New 
London Bridge, with Centering, U. 6<l. 

999. View of the Menai Suspension Bridge. By W. A. 
Frovis, Esq., C.E., &c. Fine large print, India, 10*. 

993. View of the Cast Iron Bridge across the Galton 
Canal. By R. Bridgens. Laxf^ sise, 4«. 6tf. India proofs, 6t. 

994. View of Hammersmith Suspension Bridge. Finely 
engraved, large sise. 5s. 

995. Flan and Elevation of Shrewsbury Bridge, Is. 6rf. 

996. Dr. George Meier's very Elaborate Detailed Plates 
of the Cathedral of Cologne, on nine very large sited sheets, 
showing the minutest detail to a large scale: this very fine 
structure is nearly coeval with St. Stephen's Chiq^, Glas- 
gow Cathedral, and other Edifices of the best age of Archi- 
tecture in this Country. With a test, small folio, in the 
Goman language, 4^4. 4«. 

997. Mr. Britton's Views of the West Fronts of 14 
English Cathedrab, fdio sise, 8t. ; aequatinted, 10*. 6tf. 

998. Mr. Britton's Series of Picturesque Views of the 
Interior of 14 Cathedrals, with a Border of Architectural 
and Sculptural Ornament, folio sise, 8c. 

990. Vsrdy's Perspective View of the Gothic Hall, 
Hampton Court, finely engraved, folio, 5s. 

930. Mr. Coney's View of the Interior of the Cathedral at 
Miiui, fine large print, 6f. 



931. Geometoical Elevation of the Wast Wnut of ik 
Cathedral of St. Paul's, London, before the fiie; >t 
Stephen's, Vienna; Stnsburg, Cologne, the Towsr tf 
Mechlin, and the Great Pyiamid of Eggrpt, to one a«k 
folio print, it, 

939. Flan of Westminater Hall and the w^iaccBt U» 
Courta, Is. 

933. View of the West Fh>nt of the PrapylaM at Athcw 
folio. Is. dd. 

934. M^ of Attica with part of Boeotia, improved fraa 
the observations of recent traveilera, partieolarly bv Capcsu 
Smith, R.N., 9s. 6rf. 

935. Portraits of Eminent Ardiitects and En aimci a, mez 
who have done honour to Britsin. Engvwvod^ tfe ktst 
style by superior artista, folio and 4to. ssaea, j^l. is. ckc 
Set: 

1. Sir Christopher Wren. 
9k James Stuart. 
8. Nicholas Revett. 

4. Sir WiUiam Chamben. 

5. James Watt. 

6. Humphrey Repton. 

7. Thomas TeUbnL 

8. Thomas Tkedgold. 

936. Transverse Section of the Temple of Jopitcr Otyn- 
pius at Agrigentum, folio siae, is. (M. 

937. Mr. Blair's Drawing of a Coriatfaial Chyltal, tiA^ 
grq>lied, large siie, 9t. dd. 

938. Mr. Cheffln's large Uthographed Print of the Loa- 
don and Birmingham Railway Entrance Fkont of 1^ 
London Station, 5s. 



I 



239. 
Fine large print, At. 

SHEER DRAUGHT OF HER MAJESTY'S STEAM SHIP OF 

WAR ''MEDEA,'' 

Built by Oliver Lang, Esq. at Woolwich ; first commanded by Captain H. Au8tin in the MeditexniieiD 
for nearly four years, and since on the North American station by Captain Nott. 



I 



ARCHITECTURAL LIBRARY^ 59^ HIGH HOLBORN, 



29 



PREPARING FOR PUBLICATION IN THE COURSE OF 

THE YEAR 1840. 



240. 
THE PUBLIC WORKS OF THE UNITED STATES, 

CONSTRUCTED BY EMINENT AMERICAN ARCHITECTS AND ENGINEERS; 

Consisting of Plans, Elevations, and Sectional Details of all the principal Improvements of the States. 

By WILLIAM STRICKLAND, Architect and Engineer, 
EDWARD H. GILL, and HENRY R CAMPBELL, Engineers. 

THB FOLLOVeiNG SUBJBCT8 ARJS PRBPARINO : 



Plan, Elevation, and Sections of the Bank of the 

United States, Philadelphia. 
Plan, Sections, and Details of a Locomotive Steam 

Engine, as constructed by M. W. Bald'win, 

Philadelphia. 
Plan, Elevation, and Section of the double outlet 

Lock on the Schuylkill Canal at Plymouth, 

Pennsylvania. 
Plan, Elevation, and Sections of the Schuylkill 

Viaduct on the Columbia and Philadelphia 

Railroad, Pennsylvania. 
Plan, Elevation, and Sections of a Timber Dam, 

on the Sandy and Beaver Canal, Ohio. 
Plan, Elevation, and Sections of the United States' 

Mint, Philadelphia. 
Plan, Elevation, and Sections of the Schuylkill 

Permanent Bridge, Philadelphia. 
Plan, Elevation, and Sections of the Philadelphia 

Exchange. 
Plan, Elevation, and Sections of the Philadelphia 

Gas-works. 
Plan, Elevation, and Sections of the Stone Via- 
duct over the Schuylkill River at Fhoenizville, 

Pennsylvania. 
Plan, Elevation, and Details of a Locomotive 

Steam Engine, as constructed by H. R Camp- 

beU. 
Plan, Elevation, and Section of the Philadelphia 

County Prison. 
Plan, Elevation, and Sections of a Cut Stone 

Aqueduct, constructed over the James River, 

Virginia, on the James River and Kanawha 

Improvement. 
Plan, Elevation, and Section of a Canal Bridge. 
Plan, Elevation, and Sections of the Philadelphia 

Alms-house. 
Plan, Elevation, and Sections of the Ginrd Col- 
lege for Orphans, Philadelphia. 
Plan, Elevation, and Sections of the Fairmount 

Bridge, Philadelphia. 
Plan, Elevation, and Sections of the Philadelphia 

Water-works, with a Map of its location. 
Flan, Elevation, and Details of an improved Eight- 
wheeled Day and Night Passenger Car, aa 

used on many of the Railroads in the United 

States. 



Plan, Elevation, and Sections of the United States' 

Naval Asylum, near Philadelphia. 
Plan of the Aqueduct over the Allegheny River, at 

Pittsburg, Pemisylvania. 
Plan, Elevation, and Sections of a Canal Lock, 

with improved gates, Sandy and Beaver Canal, 

Ohio. 
Plan, Elevation, and Sections of the Exchange 

Buildings at New York. 
Plan, Elevation, and Sections of the Eastern Peni- 

tentiary at Philadelphia. 
Plan of the Reservoir Mound and Gates, with 

Details, on the Schuylkill Canal, near Pottsville, 

Pennsylvania. 
Plan, Elevation, and Sections of a Cut Stone Aque- 
duct being constructed on the line of the New 

York Water-works. 
Plan, Elevation, and Details of the Troy and Sara- 
toga Viaduct and Draw constructed over the 

Hudson River, New York. 
Plan, Elevation, and Sections of the Bridge over 

the Delavrare River at Trenton, New Jersey. 
Plan, Elevation, and Sections of a Stone and 

Timber Lock, as constructed on the Schuylkill 

Canal, Pennsylvania. 
Plan and DetaUs of a Hudson River Steam Boat 

for Passengers. 
Plan and Details of the Delaware Breakwater at 

the entrance into the Bay of Delaware. 
Plan of the Timber Dam constructed across the 

Swatara Union Canal, Pennsylvania. 
Plan, Elevation, and Section of the Stone '^aduct 

at the " Horse Shoe Bend," Allegheny Portage 

Railroad, Pennsylvania. 
Plan of a Burden Car with Eight Wheeh, as used 

on the Pennsylvania Railroad. 
Plan, Elevation, and Sections of the Towing Path 

Bridge, constructed over the Schuylkill lUver at 

Manayunk, Pennsylvania. 
Plan, Elevation, and Sections of a Steam-boat 

Lock, as constructed on the Kentucky River, 

Kentucky. 
Plan and Details of a Floating Dry Dock, now in 

use on the Mississippi River. 
Plan, Elevation, and Sections of a Timber Bridge, 

as constructed by Col. S. H. Long. 



®~ 



30 



PREPARING FOR PUBLICATION BY JOHN WEALE^ 



Sections and Details of the various Rails used in 

the United States. 
Plan, Elevation, and Sections of a Cut Stone 

Aqueduct, constructed on the Chesapeake and 



Ohio Canal. 
Plan of a Lock of 30 feet lift, oon s i m ctcd on O. 
Lehigh Canal, Pennsylvania. 



The Plates will be engraved by Mr. John Le Keux in his best style, and to be sold in the sepuvt 

Divisions of A, Architecture, 

B, Mechanical Engineeiing, 

C, Civil Engineering. 

To be published on fine Imperial folio paper, in Parts of 20 Plates, faced by a particular I>escn{6^ 
of the Subject. Price £1, in England, and 5 dollars in the States. 



241. 

THE PUBLIC WORKS OF GREAT BRITAIN, 

VOL. II. 

To be published in Parts of 20 Plates, engraved by Mr. John Lb Kkux and the best EngniTers; et 
Plate to be faced by a particular Description of the Subject. Price £1. each Part. 

The following are some of the very important subjects chosen from the highly scientific iroria 
George Leather, Esq., C.E., of Leeds. 



Cast Iron Aqueduct over tke Biver Calder at Stanley 

Ferry, near Wakefield. 
Ooole Docks and Locks. 
Goole Lock Gates, with the machinery for opening and 

shutting thcui. 
Goole Bascule or Hoist Bridge. 
Hull HoUt Brid((C. 
Aire and Calder Navigation. 

— Goole Canal. 

Biver Don Navigation. 

General Flan of Aire and Calder Navigation, from 
Leeds and Wakefield to its junction with the Goole 
C^mal at Ferrybridge. 

Do. do. from. Ferrybridge to Ooole, with 

the Docks at the latter place. 
General Transverse Section of the Canals, with the 

aide walls, &c. 
Two examples of Locks,>-a Flood Lock and a Fall Lock. 
Two Stone Bridges— one square, another askew. 
One Swivel Bridge. 



A Drainaee Culvert and a Warping Sloiee. 

A set of Lock Gatea, both geosnMricaUy aad 
trically projected. 

Double acting Cloughs and Drawing Gccr. Ca^ 
and Anchors, Pivota and Steps, Forcbsty Dcfrcar 
and other Iron-work coBD«eted with the 

Lock and Bridge Keepers* Honaea. 
Dunham Bridge,— Details, Elevations, &c. 
Hunslet Bridge, Leeds. 
Astley Bridge. 
Honk Brid^, Leeds. 
Victoria Bndge, Leeds. 
Oott's Bridge, Leeds. 

Thorp Hall or Waterloo Bridge, near Leeds. 
Stockton and Hartlepool Railway. 

Public Road Bridge under. 

Occupation Brid^ under. 

Do. do. (iron). 

Sea Embankment at Straaton. 
Nocton, &c. Drainages. 



These will form 50 weU-occnpied Plates. 
The following, in continuation, of other eminent Engineers, are also in preparation. 



\ 



St. Kathcrinc's Docks — Form of Shoes used for Bay Piles 
of Coffer-dam. 

■ Form of Shoes used for Sheetinir 

Piles. 

— — — — Abutment for Swivel Bridge. 

— — ■ Dock Gates. 

Plans of Coffer-dam (2). 

- — ■ Transverse Section of Coffer-dam. 

Truss of the Roof over the Long Room, Custom House, 
London. 

Coal Jetty at Coffin's Wharf, Cardiff. 

Taff Vale BaUway CulverU. 

Pug Mill. Screw Jacks, Wliecl Barrows, Draw Crabs. 
Tram Plates. 

Weir for Bromley Mill. 

Telford's Timber Turn Bridge on the Grand Surrey Canal. 

Tewkesbury Severn Bridge. 

Centering for Balloter Bridge across the River 

Dee, Aberdeenshire. 

Splendid Drawings of various Cranes. 

Middlewich Branch of the Ellesmere and Chester Canal. 

Cross Section of Culvert for conveying the Feeder under the 
Glamorganshire Canal and Merthyr Road, and longitu- 
dinal Section. 



Pile Driving. 

Bute Ship Canal— Travelling Crane. 

— — — ^-^— Winch, Pmion Wheal, Barrel 

Tilting Wivgons. 

— — Inner Basin, Masonry 

— ' ' Communication Locks. 

—- Hollow Quoin of Entrance ^^ 

• Swivel Waggon— Stone Wmnait. 

Counterforta, Sectiona. 

■ Dock Gates, &c. 

Foundry Cranes. 

Plan and Section of the Great Sea l4>ek 
Lowestoft. 



&B.-> 



Port-Glas^w Wet Dock Lock Gate. 
Swing Bndge between outer and -inner 

Eastern Docks, Custom House, Loodon. 
Outfall at the N. W. comer of Cardiff Caade. 
Bridge at northern entrance to Cardiff Castle. 
Bridge at N. W. corner of Cardiff Castle, aero^. w^^ - . 

Bute Ship Canal. -«^»« re«..| 

Newport Road Bridge across Feeder of Bute SKi^ c»r i 

Crane at Harrison's Wharf, London, canahlfc r.f -* 

five tons, cost jff 135. ' «« .-i 



ARCHITECTURAL LIBRARY, 59, HIOH HOLBORN. 



31 



242. 

In 8vo.y with Plates, a Second Edition of 

A PRACTICAL TREATISE ON LOCOMOTIVE ENGINES 

UPON RAILWAYS; 

The construction, the mode of acting, and the effect of Engines in conveying heavy loads ; the means of 
iscertaining, on a general inspection of the Machine, the velocity with which it will draw a given load, 
ind the results it will produce under various circumstances and in different locaUties ; the proportions 
v-hich ought to he adopted in the construction of an Engine, to make it answer any intended purpose ; 
he quantity of fuel and water required, &c. ; vnth Practical Tahles, showing at once the results of the 
'onnulae: founded upon a great mant new experiments made on a large scale, in a daily 
tractice on the Liverpool and Manchester, and other Railways, with different Engines and Trains of 
carriages. To which is added, an Appendix, showing the expense of conveying Goods by means of 
A)comotive8 on Railroads. 

By COMTE F. M. G. DE PAMBOUR. 



243. 

A New Edition, with Additions, by G. Rennib, Esq., C.E., F.R.S. 

PRACTICAL ESSAYS ON MILL-WORK AND OTHER 

MACHINERY. 

n the Teeth of Wheels, the Shafts, Gudgeons, and Journals of Machines ; the Couplings and Bearings 
' Shafts ; disengaging and re-engaging Machinery in Motion ; equalizing the Motions of Mills ; 
langing the Velocity of Machines in Motion ; the Framing of Mill-Work, &c. ; with various useful 
ibles 

By ROBERT BUCHANAN, Engineer. 

rnsedf with Notes and Additional Articles, containing new Researches on varioas Mechanical Subjects, 

By THOMAS TREDGOLD, Civil Engineer. 

Illustrated by Plates and numerous Figures. 2 vols. 8vo. 



244. 
4to., Price £1. la. Corrected and enlarged. 

THE CARPENTER'S NEW GUIDE. 

ing a complete Book of Lines for Carpentry and Joinery, treating fully on Practical Geometry, 
ffits, Brick and Plaster Groins, Niches of every description. Skylights, Lines for Roofs and Domes ; 
th a great variety of Designs for Roofs, Trussed Girders, Floors, Domes, Bridges, &c. Coppcr- 
ites : including some Observations and Calculations on the Strength of Timber. 

By P. NICHOLSON. 



245. 
Fourth Edition, improved and enlarged. 8vo., Price 12«. boards. 

PRACTICAL ESSAY ON THE STRENGTH OF CAST IRON 

AND OTHER METALS; 

ended for the Assistance of Engineers, Iron-Masters, Millwrights, Architects, Founders, Smiths, 
I others engaged in the Construction of Machines, Buildings, &c. Containing Practical Rules, 
jles, and Examples, founded on a Series of new Experiments ; with an extensive Table of the 
)p€rtie8 of Materials. Illustrated by Eight Plates and several Wood-cuts. 

By THOMAS TREDGOLD, CivU Engineer. 



* * 




2 MR. WEALB'S supplementary LIST. 

WMtem Europe, Mr. Wsalb htm for lome UnM pMt been engiced In the picpentloa, under eompaCflBt eaper- 
intendenoe* off a large Oeou>oicAi« Map of 

ENGLAND, WALES, SCOTLAND, IRELAND, FRANCE. GERMANY, 
SWITZERLAND, AND PORTIONS OF ITALY, 
AND OF THE AUSTRIAN AND PRUSSIAN STATES. 

Without entering into an enumeimtkn of all the authorities which hare been ooneulted in the prepamtion of each 
a Mao. it wUl beraffldent here to state that it b baaed upon the obserratlonc of the most eminent Britld» and 
fofolni GeolofflsU, and includes in a digested form the most recent of their labours. The siie of the ICup Is as 
inches bv 264inches, dimensions which unite to oonvenienoe for reference the practicability of a aeale sulBcicBtly 
Urse to admit of the inseitlon of all the more important aeological and gcagraphical features of the ef-»*-«— 
delineated. In order to render it as much as possible an exhibition of the Phmteal Gmgraphtf as well as the 



of these oouutries, the names not only of the larger rivert, but also of their tributaries, as well as of smaller ai 
have been inserted ; and particular attention haa been given to the ooneet Indieatkm of the numerous small srmms 
and chains wliieh form parts of the mountain systems of Britain, France, Germanj, Switaerland. and Italy. The 
etoratlon attained by the higlier summits of each of the principal diains is specified In English feeU K»hihHii^ 
thus the geofrraphical as welTas geological features of the countries represented, the Map to well calculated to Ibcm 
a useful giiide In the oonsideraSon of the ▼arious lines of Rallraad whieh are either constructed or In p i ofi e ss 
throughout Tarious parts of them. 

The Map to handsomely engraved on steel, and the various geokialcal formations will be bcautifttny oolonnd fa 
aeoordanoewith the system adopted in the most recent works of KngUih geologists of e mi ne n ce. 

In sheet, eoloured, 30*. Mounted on rollerB, £> Ss. In a ease for the library. £8 Sfc 

251. 

Papers on Iron and Steel, Practical and Experimental, with copioos iUastmtiYe 
notes, by 

Dayid Mushst, Esq. 

Honorary Member of the Geological,' and the Qud>ee Literary and JlistoHeal 
Societies; of the Institution of Civil Engineers of London; Corresponding 
Men^rofihe WemerianNa,tural History Societyy Edinburgh. Lam and thick 
royal Svo volume, with several plates^ in extra doth boards^ price 1/ 10«. 

*• He has enriched hto native country with a discovery, which to Invaluable t he has suceeded by petknt and la- 
borious Investigation in evolving the properties of minerato, the moat Important to our national prosperitys and be 
has fixed the clearest principles of operation in all matters relating to the manufketure of iron and sted. It to dw 
to any one who even oardessly reflects upon the subject, that the production of iron from the Aidon and eepaitfloo of 
the parts in msMca of Iron-etone, cont^ning a fluctuating quantity of the ore sought to be extracted, must depeskl 
upon a chemical agency, and therefore upon a knowledge of combinattdn and dfisolutlon, mhkh can alone be ae- 
qulred by repeated experiments and by aecuracy of observation, and demands a knowledge of practical philoeophy, 
only to DC attained by a development of its principles, in fkct, by a discovery through an of naturefs secrec i^ 
In the manufacture of iron, therefore, the materials used, the component puts of the iron-stone Itadf, their 

upon the quality of cast-iron, the use of limestone as a deanser of earthy mixtures, an examination into thai 

produced by flie nature, compiesslon, and velocity of the Mast ; the comparative merits of cokes and **>*y*e'. the* 
very construction of the blastfurnace itself, these and a thousand other ramiflcatkms of the salijleet, mutt be the 
legftimate and anxious themes for philosophical enquiry. Unless one should be wdl acquainted with the varied 
ohaiaeter of the mineral relics contained in the bosom or the earth, the extent and benefit of Mr. Muahet^ labonn 
can hardly be appreciated. To arrive at something like definite terms, definite principles, definite knowledge, and 
definite oonduMons; In fact, to make metallurgy a science wu hto aim, and In that he has been triumphemly sve. 
oessftal— end yet it to most extraordinary that of the many iron-masters, who are dally reaping the benefit of Us 
researches, aoopting hto nomenclature, living upon hto suggestioos, and crowing rich oy hto expnienoe, there ate 
scarcely three who have any extensive and thorough acquaintance with the science. Thenapers contained in the 
magnificent volume before us, comprise the result of hto experiments fhnn time to time. The value of them to en- 
hanced by the oopfous notes appenoed to them, comprising the rssults of later experience. For Inttanoe, we have aa 
elaborate account of the application of heated air to the smelting of iron, andumesof Its efltets. Besidaa, there to 
a moat Invaluable appendix, comprdiendlng an analysto of all the ooato found in the great coal dtotricts of »"g*—^ 
where the smelting and manufocture of iron prevtfto ; an analysto justly described oy Its author as * ext e ns ile,' 
' laborious,' ' without parallel,* and we may add, of incalculable advantage to our national p r o s per ity . To give aa 
Idea of Uie fatigue endured upon some occasions, in hto experiments upon the shrinkage and expansion of cast Iran, 
Mr. Mushet presents us with the following graphic account :— * From 1S8 deg. to IMd^. I felt a aenmttai of cold 
similar to that when approaching a fire in winter, accompanied by a considerable degree of shivering. About IBO 
deg. thto sensation wore off, ana I felt oompamtively comfortable. Perqiiration had became so violeot, as to oedM 
through all parts of my watoieoat, breeches, and stodungs. The workmen who carried the metal perspired In sndi a 
manner aa to wet their large aaeking trowaers aa if they had been aoa^d in-.water. The mobture tan In anch tor- 
renta from their faces and anna aa to be dlatinctly heard hbsing upon the heated moulda. Their atep and aroM weie 
now more agitated than I had ever before otaaerved. and the ainewa all over thrtr bodica were unoonSnonly lane and 
felt inflateolto a great degreOi Two men performed the whole labour of pouring ; ro that each of them In 32 inmnln 
carried half a ton of metal in quantltlea. In hand ladles, from S0 to <0 nounda eadi time. The apaee gone thiOMh 
each time, the return with the empty ladle Included, was neariy ISO feet, or ftilly equal, upon the whole travel, to 
half an English mile; the half of which space was traversed with a todle, metal Included, weighing 80 poun^ One 
of the men immediately after thto operation, emptied- a pitdier of spring water at one draumt, whl^ I — ^i^tt^tit at 
five English pints. At the 3rd cast the thermometer rose to 164 deg. When the cest was finished I had the doon and 
windows shot. Thto made the real state of the moulds visible. The 18, 94, and S-pounders (cannon-ball) were aO 
of a dtf k glowing red heat, and presented an arid and Inhospitable glare, with whidi It was Impoesible long to exist.* 
(pp. 808, C) What will the Chaberu and other fire-kinga say to thto i Would the oven of the llluscriou^rsnclunan, 
co-tenant with hto beef-steak, have produced by Ita cooking heat and eflbet graeter than the following, expettotteed 
by the son of science ?—' One day a spirit of wine thermometer burst In my hand with a report like a pisiol :* p. 
SOU We must mention the discovery of the Blackband, or Mushet'etone. alhided to above, as one InMance aaoM 
many of the st^id advantages derived from Mr. Mushef s researehes to the country at large, and for which he hS 



. tageai 

earned that which will no doubt be dieerfully aoeordcd to him, tiie enthualaatie gratitude of the preeent ^ 

and of a posterity yet to comcb • The dtoeovery of thto stone was made In 1801, when I was engsged In ereettaMfov 



myself ana partoers the Calder Iron Works. Chneat prejudice waa excited againat me by the tron<maalen and 

ofuat day m preauminc to claaa the uriii coato of the country with iron-aton«s fit and proper for the btasMtamaee. 
Yet that discoTery has cdevated Scotland to a consldemMe rank amongst the iron-making nations of Bnrope^ with 
resources still In store that may be considered inexhauatlblek But such are the eoneolatory eflbeta of tfane net Che 
<iiaooverer of 1801 to no longer oonaideted the intruaive visionary of the laboratory, but the acknowledged beneihelor 
Ma country at large, and particularly of an extenalve daas of eoal and mine pro p itetuii and Iron maalrfi. who^svt 



ItB. WBALB*S STTPPLBMEMTAHY LIST. 



Dt illKDVcryi And who, ki thti^ilt of fnttaAil Kkoow- 
• luoBumBital ncvd Dpan tbe not wbtn tb* dbciRBy 

,T^jtt thiDUfllHHit the po*< of Uni Kdiime» In m nnlu 

UU..V— ■ — - wworM. by ensourtg&a Ihaiouiuactiin sf Inn upon putoia- 

Ilr.HiabMmnlmgttnioniliTTtlwCiiuhahuiMuInd, and to iMp.tb* buiot tf Ua bowBu Iw hat ddW«t- 
uUf .imif-rf» riii»riiiwift*ii CArnUfi Sfpt. M. IMdL 



d m Uill doMn* cnM naldi ftom Ihli 
)u** pTODouDCMli mitt[*o(icra«aof| 
lada. TPRtUa p. xtU.] Thu tbe liifiinu 
td Item , will b> of onlUI wnlca (D th* ' 



252. 

Papbbs on Subjects ' connected with the Duties op thk Corps of Royal Bm- 
aiHEZBS, Vol. IV., 4U>, 30 ptatet, extra cfoM bound, U St. 

CONTENTS. 




Ntw Wilfh BrUn in Woolni^ Doek-Twd. 
Single CoAeduntn Dltto- 
-Wln)eellii( Cmml Into La] - ■ ■ — 
Hi tbe EmplfmueDt of Send 



TtaSii^ 



4 by the BulUiley Cora- 

* lUUny Inn Br»d« onr lb* 

u 5>-l>y, by tbe Bu&edey Ctn- 

« lata Ciptmla DrommoDd, It.E., I 



253. 

Ornamental Ibon Wokk, Qatea, Lodges, Palisading, &c., of the Boyal Parks, in- 
cluding the Plans of Regent's, Hyde, St. James's, and Qreen Parka, with the 
Entntnces to the Sultan's Palace at Constantinople, 50 pUuet, in^erial 4to, 
with a letter-press description of the recent ImproTements in the Perks, and 
the £ntrtu)ce into London, haif-bouitd in momxo, price 2l 8t, 



.W,,! 



TBI POLLOWINQ IB 
mm* tD St. Juw^i Fuk. 



m of Renni'i Park. 

irbti ARta, Buckis^um Fakeei plu u 



Lodge of diUo. plu 
ide. Hyde ■>»■, e 
indeleTUlDD- 



10. Hyde Puk Lddge, noni ud it 

11. HmnuM Sodety ReeelTlng Hoin 



t, OneeeDOT Lodge, front md 
3. SUnbovfl Lodge, fie-' — '' 



X. Lunp ud ItiUina, Chelien HonlUL 

aPuti of Inn Wok ditto, to • iHHr iMta. 
OMf, lUmpMBCaun, ISli C. Wnn.) 
36. Dltta, ditto, dHIo, 

M. Put! of lioB Woih, ditto, dlua 
<l. Inn Work dfKtnu'iStelRM.dltta. 

ti, PUn ud El*ntiOB of EMnsii* Lodax a&d Ii 
Oetee at Onenwleb, (Sir C Wien.) 

U. IHttD, dliia.laifcriMla. 

4L Inn Oatei at OoDDanbury Pavk. 

td. Plu.ElwrMkn.aadDelaiUofdJtta. 

n. old BucUntflani Palaa EntTiiu, Inn OMee 
17S7. 

48. Lamp, Stirlb« CiMla. 



■ide elermtUnu and plan. 

tt Lodge, elrvaUon end ptau. 

I& Hanorer Lodn. alevatlon aod plan, 
17. Lamp at Hyde Paik Corner, with ihe detail*. 
la Galea centre o/ Cdonnade. HydaPaik. 
la IMailiafdIIto, quartet Mil iit. 
so. nallincaltbehead of On BerpoiDne Rlier, Dmf 
Oatea to Royal EntiaDca, DwaifRalUnf to Lodge, 

n. Sun£opa Gate Ralli, Hyde fttk. 
sa Cunbetland OWa Ralli, Hyde Paik. 
ti. Paila and Detalta of pReedlnc. 
W. RaUlai, Puk Squaie, RopsFi Patk. 

With two beautiful »ood-eutt by Mr. Smith, of the past and present En- 
trances at Hyde Park Corner, suggested for insertion, and the Drawings 
contributed by Decimos Burton, Esq., Architect, to whom Mr, Weale is much 
indebted for other contribnttons. 

254. 

Appendix A. and B. to TREDOOLn on Steak Navioaiiq„ ^tlas folio, with descriiptiTe 
letter-press to both in 4to. The plates, 22 in Q.^.-.'bet) eibiW verj e\a>»iaie 
d Timber Boats with the tT^ifli Unsoc, ■price ll 12*. 



subjects of Iron and Timber Boats with the » 
Appendix B. separate, for those who have b<t^J 






4 MR. WBALB^S SUPPLEMBNTABY LIST. 

255. 
DOMESTIC ARCHITECTURE. 

A SBRnts, with a particular deseription, of rery tagteftil examples of Interiots and 
Exteriors of the Residences, of the Gentry erected in HambuiKh and its net^- 
bourhood, principally in the Italian style, with Ornamental Pleasure Groimdsy 
Verandas, Detached Cottages, &c., 19 fine jpiateM by A. de Chateaoneaf, in 
large 4to, extra do^ boardi^ priee 1/ 1«. ; in large folio, with proof jdaies, 
\l \U ed. 

256. 

LoKDON and Staines Bbidobs, magnificently drawn in Elevations and Plana, by 
B. Albano, Esq., C.E^ and engraved in the finest style of art by Lowiy and 
Le Keux, large size. London, 1 8«.— Staines, 12«. 

257. 

A Catalooub of Books on the subjects of Abghitbctubb ; Enoikbbbino, Civil, 
MiLiTABY and Mbchanical; Naval Arghitigturb, and the Arts and 
Manufactubbs of the Country ; classed, with an Index, by John Weale, 
in 8vo, price 2« 6d. 

258. 

The Travellers' Club Housb, designed and executed by Charles Bany, Esq., 
Architect, with an Essay on the present state of Architectural Study and the 
reyiTal of the Italian Style in Great Britain, by W. H. Leeds ; very fine plates 
by Le Keux, consisting of Plans, Elevations, and Details, large 4to, kalf- 
bound in moroocOy price 18«. 

*< This is the oommeooenient of a publkfttloii ealculated to viadieite the duneter of EngUah ai^ilteets. aiid to 
adT«noe the Mienoe of architecture itwIH * One material diflbrenoe, aa7> the preboe* ' between it and Merlous 
woriu of the Jdnd whldi have been brought out in this eountry. whether as eoHections of buildfai^ br iJifliiin m 
ardiitects, or the designs of an individual, is the completeness with whldi the buUdlnc selected for the vurpoee it 
illustrated and elucidated, not only with rtgard to sections, as well as plans and elev^ioas, but also by oetaus and 
parts at large \ without which latter the ot&r drawings lose much of their value, perhaps are in some ili^pM rather 
Injurious to the youthftil student, because only the goleral fonns are presented to him i the oonseiiueniae of whkh 
is that sufficient attention is not paid by him to that kind of character, and to that finish, wlildi depend imoo 
detaiL' 

*< Mr. Leeds begins his ' Essay on Modem English Architecture* by adverting to 'the peenliar, not to say 
equivocal, position of archlteetun, occasioned by its compound character of a medianiosi and a tee art/ and to 
the disadvantages to which it has been sutiject in oonsequenee. He proceeds to observe that, * looking at what has 
been done within the last twenty or flve^ind-twenty yeers, although among the buildings erected within that peitod 
we meet with many of considerable merit, we also ehoounter not a few that are quite the reverse eeitainly, very 
far Inferior to what they might have bcw rendered by more diligent study and more artistlike treatinenL' He une^ 
as a stimulus to exertion on tlie subject, that * it should be borne In mind that the eyes of fore^picrs are upon h, 
who, while they contemplate with astonishment of one kind our worlu of utility, our bridges, eaaals, tunnels, 
raihroads, and constructions of that class, generally 'egerd with astonishment of a very different kind those of our 
buildings in whidi, if any where, grandeur and reflnedtaste mi|dit be expected to display thcmselvt 

'r,es the French express it, of the IHill" ' 



** The general idea, or motif, ts the Frendi express it, of the nil Mall Ront, appears to be derived ftom that of the 
Palaiso Pandolflnl at Fknenoe, the design of which Is attributed to Raphael. Instead, however, of at all a — ,.j.^ ^ .gf 
from the origiiuUity of the English bmlding, the reeemblance that may be traced between the two servea only to 
shew how mudi the beadties of a model may be improved upon by a frae imitation of it in the hands of a niMler. 
There Is a siw K e s se In the English palaaeo, which the Italian one does not possess, and more variety In lis Indlvidnal 
Dsatures t it has also more unity m diaracter. It Is free from that heaviness in its general proportions, and fkom 
dryness of style in the details, which merit Its archetype; and It further derives no small degree of addlttanal 
elegance from the temodlke screen to the area, which converts into a podtive beauty— a graocftil, as well as a 
pietureeque accompaniment— what Is almost taivariably alk>wed to be more or less a blemish. While it aeadsds so 
perfectly with the other in Ita taste, that it would be ImposdUe not to recognise it Immediately as the productiaB ot 
the same mind, even were It not known that the two elevations bdong to the same building, the garden fje^ade »^»m« 
the iinpress of greater originality. The piquant dtteX produced by groupiiig together the three centre wlndowi of 
each floor is as happy as it is unusual : this eompodtfon has an indeflnabfe charm, an attractive mm le dhe of 
sentiment. Infinitely more captivating than that mere pomp of aidiitecture, which is frequently to be met with la 
dtesigns thist, nevertheless, betray complete Inanity of ideas. Those who may be so disposed are at Ubeity to ssy 
that there is not iqudi in it, after all— merely a few windows and rustics, and some other members of detail; la 
short, nothing m<ffe than what any one else might have done. Very truei but, then, how are we to dlnwee of the 
untoward question. Why have they not done so r Why should they— those, at least, who have practised the Italiaa 
style— have forborne to avail themselves of it to the extent we now perodve it was posdble for them to have done, 
had they been capable of bringing to It that geniality of feeling and taste, without which a work of aidiltcetufe 
can never bea work of art, except of art at second-Jiand ; whatever it may be as a production of manual labour and 
mechanical skill ? « • • e 

« One quality in which this building to pre-eminent, and at present stands almost alone. Is the perfoct JbsM 



(« 



bestowed on every part. There Is not a dngie member, let Its situation be what it may, wliidi is not nibet earefuOy 
studied and workra up, as will be evident on examining the plates of details i and, unices they are carefully ieeked 
at, the merit of the elevations, particularly of that of the nrden front, cannot be ftilly appreciated in all tMr 
piuticulars. TKls quality of teish can haraly be too strongly insisted upon, because It li precisely the very cne of 
whidi we are apt to be careless. Hence the almost inexcusable inequalities which offiBOd the eye in eo many 
structures otherwise not devoid of merit : paltry and misplaced economy In one put Is suflbrsd to Interfere with the 
embellishment bestowed on others, and which is thereby sometimes rendered little better than tnmpcry and 
misplaced ostentation. No doubt, some parts of a compodtlon, particularly where the dcdgn ie of 
-'-- ^ " -.^^. OTy different thing ftom ^ '" 



tent, ought to be treated as subordinate to others t but that to a very different thing ftnsb ncgtactiiig i«»., «•<»»« 
last serves only to render them all the more conspicuous and obtrusive aa blemishes and seaie la the dasin, 
las carefUl finish would have brought them foto proper keeinng with the net* 
hB plates are beautifully execute^**— Liisrary Oeceffe. 



» * 




k